1,1

Interprimes which are of the form s*prime are in A075277-A075296 (s = 2-21). Case s = 1 is impossible.

7646 is an interprime and 7646/2 = 3823 is prime.

s=2; Select[Table[(Prime[n+1]+Prime[n])/2, {n, 2, 1000}], PrimeQ[ #/s]&]

Cf. A075277--A075296.

Sequence in context: A123055 A028273 A024471 this_sequence A159557 A054094 A123873

Adjacent sequences: A075274 A075275 A075276 this_sequence A075278 A075279 A075280

easy,nonn

Zak Seidov (zakseidov(AT)yahoo.com), Sep 12 2002

1,2

Conjecture: a(3n) = 0. No other term is zero.

a(3n)=0: consider the sum of the digits modulo 3. For the same reason, if a(m) is divisible by 3 then a(m)=0. - Sam Alexander (amnalexander(AT)yahoo.com), Nov 15 2003

XIAO Gang, Factoris - a program that factorizes huge integers, 1997-1999

a(2) = 2 as 229 is a prime. but 119 is not.

s[b_]:=(v={}; l=Length[b]; Do[v=Join[v, IntegerDigits[b[[k]]]], {k, l}]; v); a[n_]:=If[Mod[n, 3]!= 0, (For[m = 1, ! PrimeQ[10*FromDigits[s[Table[m, {n}]]] +9], m++ ]; m), 0]; Table[a[n], {n, 90}] (Firoozbakht)

Cf. A086920, A087604, A087605, A087607, A087608, A087609, A087610.

Sequence in context: A060277 A101672 A083731 this_sequence A116799 A057556 A112761

Adjacent sequences: A087603 A087604 A087605 this_sequence A087607 A087608 A087609

base,nonn

Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 18 2003

More terms from Sam Alexander (amnalexander(AT)yahoo.com), Nov 15 2003

More terms from Farideh Firoozbakht (mymontain(AT)yahoo.com), Feb 04 2005

1,3

A string and its reverse are considered to be equivalent.

M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia.

A005418(n+1)-2.

Cf. A005418.

Sequence in context: A008374 A008240 A008375 this_sequence A007784 A008204 A080287

Adjacent sequences: A056306 A056307 A056308 this_sequence A056310 A056311 A056312

nonn

Marks R. Nester (nesterm(AT)dpi.qld.gov.au)

0,3

S. Hedayat, N. J. A. Sloane and J. Stufken, Orthogonal Arrays, Springer-Verlag, NY, 1999, p. 249.

Constructed recursively: subsets that include n are obtained by appending n to all earlier subsets.

empty; 1; 2; 1 2; 3; 1 3; 2 3; 1 2 3;...

(C:) #include <stdio.h> #include <stdlib.h> #define USAGE "Usage: 'A048794 num' where num is the largest number to use creating sets.\n" #define MAX_NUM 10 #define MAX_ROW 1024 int main(int argc, char *argv[]) { unsigned char a[MAX_ROW][MAX_NUM]; signed short old_row, new_row, i, j, end; if (argc < 2) { fprintf(stderr, USAGE); return EXIT_FAILURE; } end = atoi(argv[1]); end = (end > MAX_NUM) ? MAX_NUM: end; for (i = 0; i < MAX_ROW; i++) for ( j = 0; j < MAX_NUM; j++) a[i][j] = 0; a[1][0] = '1'; new_row = 2; for (i = 2; i <= end; i++) { sprintf(&a[new_row++ ][0], "%d", i); for (old_row = 1; a[old_row][0] != (i+48); old_row++) { sprintf(&a[new_row++ ][0], "%s%d", &a[old_row][0], i); } } fprintf(stdout, "Values: 0"); for (i = 1; a[i][0] != 0; i++) fprintf(stdout, ", %s", &a[i][0]); fprintf(stdout, "\n"); return EXIT_SUCCESS; }

Cf. A048793.

Sequence in context: A082827 A072484 A113698 this_sequence A164869 A082292 A164857

Adjacent sequences: A048791 A048792 A048793 this_sequence A048795 A048796 A048797

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Larry Reeves (larryr(AT)acm.org), Apr 11 2000

1,1

For an even base there are no even pseudoprimes.

a(n)=Min{x=even number; Mod[ -1+n^(x-1), x]=0}

n=2, 2n-2=3 as base, smallest relevant power is -1+2^(286-1) which is divisible with 286.

Cf. A007535, A090986-A090089.

Sequence in context: A134786 A074309 A113256 this_sequence A110816 A112322 A110071

Adjacent sequences: A090085 A090086 A090087 this_sequence A090089 A090090 A090091

nonn

Labos E. (labos(AT)ana.sote.hu), Nov 25 2003

0,2

n^4/24 + n^3/12 - n^2/24 + 11*n/12 + 1.

Sequence in context: A034749 A053024 A090166 this_sequence A018102 A018103 A123720

Adjacent sequences: A101335 A101336 A101337 this_sequence A101339 A101340 A101341

nonn,easy

Eugene McDonnell (eemcd(AT)mac.com), Dec 24 2004

1,2

The index of n is 2^n for n<10. After 9 if n ( like 13, 23) has appeared earlier it will not appear but it will be used in the concatenation at its turn as mentioned above. needs better description.

The sequence contains groups of integers generated from seeds s=1,2,3,4,... A group is the sorted list of numbers defined by the seed and all concatenations of integers of previous groups with the seed, discarding any duplicates. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 31 2007

The group 4, 14, 24, 34, 124, 134, 234, 1234 is generated from the seed s=4 itself and attaching s=4 to the previous elements 1, 2, 12, 3, 13, 23, 123, that is 14, 24, 124, 34, 134, 234, 1234, then sorting within the group (moving 34 between 24 and 124).

Cf. A113699.

Sequence in context: A012629 A082827 A072484 this_sequence A048794 A164869 A082292

Adjacent sequences: A113695 A113696 A113697 this_sequence A113699 A113700 A113701

base,nonn

Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 11 2005

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 31 2007

2,1

a(1) doesn't exist because 1 is coprime to all integers.

a(p) = 2p, for all primes p.

Sequence in context: A104123 A094078 A016122 this_sequence A155750 A159475 A098350

Adjacent sequences: A160992 A160993 A160994 this_sequence A160996 A160997 A160998

nonn

Leroy Quet (q1qq2qqq3qqqq(AT)yahoo.com), Jun 01 2009

Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Jun 13 2009

0,2

Sequence in context: A066185 A008107 A057306 this_sequence A104385 A062479 A007009

Adjacent sequences: A047729 A047730 A047731 this_sequence A047733 A047734 A047735

nonn,easy

Patternfinder(AT)webtv.net (Robert Newstedt)

0,4

I. L. Hofacker, P. Schuster and P. F. Stadler, Combinatorics of RNA secondary structures, Discrete Appl. Math., 88, 1998, 207-237.

P. R. Stein and M. S. Waterman, On some new sequences generalizing the Catalan and Motzkin numbers, Discrete Math., 26, 1979, 261-272.

M. Vauchassade de Chaumont and G. Viennot, Polynomes orthogonaux et problemes d'enumeration en biologie moleculaire, Publ. I.R.M.A. Strasbourg, 1984, 229/S-08, Actes 8e Sem. Lotharingien, pp. 79-86.

M. Vauchassade de Chaumont and G. Viennot, Polynomes orthogonaux at problemes d'enumeration en biologie moleculaire, Sem. Loth. Comb. B08l (1984) 79-86.

G.f.=G=G(z) satisfies G=1+zG+z^2*G[G-1-zG+z/(1-z)].

a(4)=4 because we have HHHH, UHDU, HUHD and UHHD; a(6)=16 because among all 17 peakless Motzkin paths of length 6 (see A004148) only (UHU)HDD does not qualify.

G:=(1-2*z+2*z^2-2*z^3-sqrt(1-4*z+4*z^2-4*z^5+4*z^6))/2/z^2/(1-z)^2: Gser:=series(G, z=0, 35): 1, seq(coeff(Gser, z^n), n=1..32);

Cf. A004148.

Sequence in context: A006211 A101333 A023421 this_sequence A084637 A100137 A141366

Adjacent sequences: A098048 A098049 A098050 this_sequence A098052 A098053 A098054

nonn

Emeric Deutsch (deutsch(AT)duke.poly.edu), Sep 11 2004