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Search: id:A083956
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| A083956 |
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a(n) = sum of all cyclic permutation of concatenation of first n numbers. In each case the digits of a number are kept together for n>9. |
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+0
12
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| 1, 33, 666, 11110, 166665, 2333331, 31111108, 399999996, 4999999995, 509876543215, 52098641976336, 5331076296399558, 546238942849832881, 56038035699304276305, 5755318721445859729830, 591693488306202516193456
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Intial terms are {n(n+1)/2}*{A000042(n)}.
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EXAMPLE
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a(1) = 1, a(2) = 12+21, a(3) = 123 + 231 + 312 = 666.
a(11)=1234567891011+2345678910111+..+1011123456789+1112345678910
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MAPLE
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# count digits in positive integer number digs := proc(inp::integer) local resul, shiftinp : resul := 1 : shiftinp := iquo(inp, 10) : while shiftinp > 0 do resul := resul+1 : shiftinp := iquo(shiftinp, 10) : od : RETURN(resul) : end: # provide number of concatenation up to lst, permuted by cycl newnum := proc(lst::integer, cycl::integer) local resul, i, insrt : resul := 0 : for i from 1 to lst do insrt := ((i+cycl-1) mod lst) +1 : resul := resul*10^digs(insrt)+insrt : od : RETURN(resul) ; end : n := 2 : while n < 13 do su := 0 : for cycl from 0 to n-1 do # print(n, " add ", newnum(n, cycl)) ; su := su + newnum(n, cycl) : od : printf("%a, ", su) : n := n+1 : od : - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 13 2006
A083956 := n -> add( convert( cat( 'modp(j+i, n)+1' $ j=1..n ), decimal, 10), i=1..n ); - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Nov 08 2006
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CROSSREFS
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Cf. A083957, A094761.
Sequence in context: A076684 A004328 A094760 this_sequence A091462 A028210 A028205
Adjacent sequences: A083953 A083954 A083955 this_sequence A083957 A083958 A083959
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KEYWORD
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base,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), May 10 2003
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 13 2006
More terms from M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Nov 08 2006
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