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A165307 Minimum number n, not already present, that permits the cyclic repetition of the path 1,2,3,4,5,6,7,8,9 of the digits in the sequence. +41
8
1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 34, 56, 78, 91, 23, 45, 67, 89, 123, 456, 789, 1234, 567, 891, 234, 5678, 912, 345, 678, 9123, 4567, 8912, 3456, 7891, 2345, 6789, 12345, 67891, 23456, 78912, 34567, 89123, 45678, 91234, 56789, 123456, 789123, 456789, 1234567 (list; graph; listen)
OFFSET

1,2
EXAMPLE

Starting from 1,2,3,4,5,6,7,8,9 the next number must be 12 because after 1,2,3,4,5,6,7,8,9 we shall continue with a 1. But 1 is already in the sequence so we need to add a 2 -> 12. And so on.

CROSSREFS

A165300-A165306

Sequence in context: A032575 A038186 A118575 this_sequence A081549 A085889 A094823

Adjacent sequences: A165304 A165305 A165306 this_sequence A165308 A165309 A165310

KEYWORD

easy,nonn,uned

AUTHOR

Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Sep 14 2009

A078193 In the following triangle the n-th row contains n n-digit (or (n-1)-digit) numbers whose concatenation (with a 0 prefixed for (n-1)-digit numbers) gives a sub-string of the cyclic concatenation of 1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,1,2,...: 1; 12 34; 123 456 789; 1234 5678 9012 3456; 12345 67890 12345 67890 12345; ... Sequence contains the final terms of rows. +41
3
1, 34, 789, 3456, 12345, 123456, 3456789, 78901234, 345678901, 1234567890, 12345678901, 345678901234, 7890123456789, 34567890123456, 123456789012345, 1234567890123456, 34567890123456789, 789012345678901234, 3456789012345678901, 12345678901234567890 (list; graph; listen)
OFFSET

1,2
COMMENT

Leading digit is [(n-1)*n+1] mod 10, zero allowed and therefore one more than the least significant digit in A002378(n-1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 19 2006

PROGRAM

(PARI) A078193(n)= { local(a, f) ; a= (n*(n-1)+1) %10 ; f=a ; for(i=1, n-1, a=Str(Str(a) Str((f+i)%10)) ; a=eval(a) ; ) ; return(a) ; } { for(n=1, 20, print1(A078193(n), ", ") ; ) ; } - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 19 2006

CROSSREFS

Cf. A078194, A078195.

Sequence in context: A028023 A025190 A160315 this_sequence A063843 A020535 A134500

Adjacent sequences: A078190 A078191 A078192 this_sequence A078194 A078195 A078196

KEYWORD

base,nonn

AUTHOR

Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 21 2002

EXTENSIONS

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 19 2006

A078194 In the following triangle the n-th row contains n n-digit (or (n-1)-digit) numbers whose concatenation (with a 0 prefixed for (n-1)-digit numbers) gives a sub-string of the cyclic concatenation of 1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,1,2,...: 1; 12 34; 123 456 789; 1234 5678 9012 3456; 12345 67890 12345 67890 12345; ... Sequence contains the triangle by rows. +41
3
1, 12, 34, 123, 456, 789, 1234, 5678, 9012, 3456, 12345, 67890, 12345, 67890, 12345, 123456, 789012, 345678, 901234, 567890, 123456, 1234567, 8901234, 5678901, 2345678, 9012345, 6789012, 3456789, 12345678, 90123456, 78901234, 56789012 (list; graph; listen)
OFFSET

1,2
MAPLE

A078194 := proc(n, m) local istrt, iend, resul ; istrt := ( 1+m*n ) mod 10 ; iend := istrt+n-1 ; resul := istrt ; for i from istrt+1 to iend do resul := 10*resul+ (i mod 10) ; od ; RETURN(resul) ; end: for n from 1 to 10 do for m from 0 to n-1 do printf("%d, ", A078194(n, m)) ; od ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 01 2007

CROSSREFS

Cf. A078193, A078195.

Sequence in context: A124705 A126366 A009760 this_sequence A034510 A083101 A133294

Adjacent sequences: A078191 A078192 A078193 this_sequence A078195 A078196 A078197

KEYWORD

base,easy,nonn

AUTHOR

Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 21 2002

EXTENSIONS

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 01 2007

A078195 In the following triangle the n-th row contains n n-digit (or (n-1)-digit) numbers whose concatenation (with a 0 prefixed for (n-1)-digit numbers) gives a sub-string of the cyclic concatenation of 1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,1,2,...: 1; 12 34; 123 456 789; 1234 5678 9012 3456; 12345 67890 12345 67890 12345; ... Sequence contains the sum of the terms of a row. +41
3
1, 46, 1368, 19380, 172815, 2850726, 37418526, 454097638, 4765432105, 12345678900, 512345678896, 5923681144786, 63692581470363, 739280583613920, 5739962954073990, 83052749708305266, 874185296307418521 (list; graph; listen)
OFFSET

1,2
MAPLE

A078194 := proc(n, m) local istrt, iend, resul, i ; istrt := ( 1+m*n ) mod 10 ; iend := istrt+n-1 ; resul := istrt ; for i from istrt+1 to iend do resul := 10*resul+ (i mod 10) ; od ; RETURN(resul) ; end: A078195 := proc(n) local m ; add( A078194(n, m), m=0..n-1) ; end: for n from 1 to 25 do printf("%d, ", A078195(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 01 2007

CROSSREFS

Cf. A078193, A078194.

Sequence in context: A060561 A066403 A028574 this_sequence A103725 A115608 A162889

Adjacent sequences: A078192 A078193 A078194 this_sequence A078196 A078197 A078198

KEYWORD

base,easy,nonn

AUTHOR

Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 21 2002

EXTENSIONS

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 01 2007

A091331 Natural numbers written out with their digits grouped in triples (leading zeros omitted). +41
1
123, 456, 789, 101, 112, 131, 415, 161, 718, 192, 21, 222, 324, 252, 627, 282, 930, 313, 233, 343, 536, 373, 839, 404, 142, 434, 445, 464, 748, 495, 51, 525, 354, 555, 657, 585, 960, 616, 263, 646, 566, 676, 869, 707, 172, 737, 475, 767, 778, 798, 81, 828, 384 (list; graph; listen)
OFFSET

1,1
CROSSREFS

Sequence in context: A001703 A004945 A004965 this_sequence A031689 A074303 A077379

Adjacent sequences: A091328 A091329 A091330 this_sequence A091332 A091333 A091334

KEYWORD

base,easy,nonn

AUTHOR

J. Taylor (integersfan(AT)yahoo.com), Mar 01 2004

A135643 Straight-line numbers > 99. +40
12
111, 123, 135, 147, 159, 210, 222, 234, 246, 258, 321, 333, 345, 357, 369, 420, 432, 444, 456, 468, 531, 543, 555, 567, 579, 630, 642, 654, 666, 678, 741, 753, 765, 777, 789, 840, 852, 864, 876, 888, 951, 963, 975, 987, 999, 1111, 1234 (list; graph; listen)
OFFSET

1,1
COMMENT

Numbers with more than two digits whose digits are in arithmetic progression. The structure of digits represent a straight line. In the graphic representation the points are connected by imaginary line segments. For a(1) to a(45) this sequence is equal to A034840. If the member of this sequence is greater than 9876543210 then the member is a repdigit number A010785.

Note that the sequence of straight-line numbers stars: 10, 11, 12, ..., 98, 99, 111, 123,... The integers with 2 digits are always straight-line numbers, but here the numbers < 100 are omitted. [From Omar E. Pol (info(AT)polprimos.com), Nov 14 2009]

EXAMPLE

The number 3579 is straight-line number:

. . . 9

. . . .

. . 7 .

. . . .

. 5 . .

. . . .

3 . . .

. . . .

. . . .

. . . .

CROSSREFS

Cf. A010785, A034840.

Cf. A135600, A135601, A135602, A135603, A135641, A135642, A163278, A167847. [From Omar E. Pol (info(AT)polprimos.com), Nov 14 2009]

Sequence in context: A133786 A039990 A034840 this_sequence A070798 A095613 A108721

Adjacent sequences: A135640 A135641 A135642 this_sequence A135644 A135645 A135646

KEYWORD

nonn

AUTHOR

Omar E. Pol (info(AT)polprimos.com), Nov 30 2007, Dec 09 2008, Nov 14 2009

A033075 Numbers n with property that all pairs of consecutive base 10 digits differ by 1. +40
8
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 21, 23, 32, 34, 43, 45, 54, 56, 65, 67, 76, 78, 87, 89, 98, 101, 121, 123, 210, 212, 232, 234, 321, 323, 343, 345, 432, 434, 454, 456, 543, 545, 565, 567, 654, 656, 676, 678, 765, 767, 787, 789, 876 (list; graph; listen)
OFFSET

1,2
CROSSREFS

Sequence in context: A085135 A085133 A110806 this_sequence A132577 A044960 A044822

Adjacent sequences: A033072 A033073 A033074 this_sequence A033076 A033077 A033078

KEYWORD

nonn,base

AUTHOR

Clark Kimberling (ck6(AT)evansville.edu)

A034840 Concatenation of 3 or more numbers in arithmetic progression. +40
4
111, 123, 135, 147, 159, 210, 222, 234, 246, 258, 321, 333, 345, 357, 369, 420, 432, 444, 456, 468, 531, 543, 555, 567, 579, 630, 642, 654, 666, 678, 741, 753, 765, 777, 789, 840, 852, 864, 876, 888, 951, 963, 975, 987, 999, 1050, 1062, 1074, 1086, 1098 (list; graph; listen)
OFFSET

0,1
CROSSREFS

Sequence in context: A104155 A133786 A039990 this_sequence A135643 A070798 A095613

Adjacent sequences: A034837 A034838 A034839 this_sequence A034841 A034842 A034843

KEYWORD

nonn,base

AUTHOR

Erich Friedman (erich.friedman(AT)stetson.edu)

A090910 a(n+1) is the least positive integer k such that 1) k is a one-digit number or the concatenation of two or more consecutive numbers; 2) |k-a(n)| is prime; 3) k is not already in the sequence; and 4) |k-a(n)| is not the absolute difference of two previous consecutive members of the sequence. +40
4
1, 3, 6, 23, 4, 9, 2, 45, 8, 67, 56, 123, 34, 5, 78, 7, 234, 1415, 1234, 1011, 910, 89, 456, 1213, 12, 2345, 678, 2425, 3456, 1819, 123456, 2627, 45678, 4445, 101112, 3031, 5678, 345, 1516, 789, 1718, 567, 2728, 100101, 2324, 4567, 1314, 891011, 4344 (list; graph; listen)
OFFSET

0,2
EXAMPLE

12 follows 23 as 23-12 = 11 is prime.

CROSSREFS

Cf. A090911, A090912.

Sequence in context: A148642 A049415 A029848 this_sequence A151443 A148643 A148644

Adjacent sequences: A090907 A090908 A090909 this_sequence A090911 A090912 A090913

KEYWORD

base,nonn,easy

AUTHOR

Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Dec 15 2003

EXTENSIONS

Edited and extended by David Wasserman (wasserma(AT)spawar.navy.mil), Feb 14 2006

A090911 a(n+1) is the least positive integer k such that 1) k is a one-digit number or the concatenation of two or more consecutive numbers; 2) |k-a(n)| is prime; and 3) |k-a(n)| is not the absolute difference of two previous consecutive members of the sequence. +40
4
1, 3, 6, 1, 8, 45, 2, 789, 56, 3, 34, 5, 78, 7, 234, 1, 12, 1213, 456, 7, 1314, 23, 4, 45, 1516, 5, 234, 23, 6, 67, 8, 345, 34, 123, 56, 9, 1112, 3, 910, 23, 456, 67, 234, 1415, 6, 89, 456, 2345, 4, 567, 1718, 9, 2122, 23, 1516, 89, 910, 1011, 2, 2223, 10111012, 1415 (list; graph; listen)
OFFSET

0,2
CROSSREFS

Cf. A090910, A090913.

Sequence in context: A118948 A118012 A022836 this_sequence A108813 A108591 A110119

Adjacent sequences: A090908 A090909 A090910 this_sequence A090912 A090913 A090914

KEYWORD

base,nonn,easy

AUTHOR

Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Dec 15 2003

EXTENSIONS

Edited and extended by David Wasserman (wasserma(AT)spawar.navy.mil), Feb 14 2006

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Last modified February 9 11:24 EST 2010. Contains 172296 sequences.

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