A007923 Lengths increase by 1, digits cycle through positive digits.

1, 23, 456, 7891, 23456, 789123, 4567891, 23456789, 123456789, 1234567891, 23456789123, 456789123456, 7891234567891, 23456789123456, 789123456789123, 4567891234567891, 23456789123456789, 123456789123456789

Offset

1,2

References

C. Ashbacher, Some Problems Concerning the Smarandache Deconstructive Sequence, J. Recreational Mathematics, Vol. 29, No. 2, pages 82-84.

K. Atanassov, On the 4th Smarandache Problem, Notes on Number Theory and Discrete Mathematics, Sophia, Bulgaria, Vol. 5 (1999), No. 1, 33-35.

Links

John Cerkan, Table of n, a(n) for n = 1..994

K. Atanassov, On Some of Smarandache's Problems

F. Smarandache, Only Problems, Not Solutions!

Eric Weisstein's World of Mathematics, Smarandache Sequences

Formula

a(n) = (10^9+1) a(n-9) - 10^9 a(n-18), n>=18. - corrected by Michael Somos, Sep 28 2002

a(n) = Sum_{i=1..n} ((n*(n-1)/2+i-1 mod 9)+1)*10^(n-i). - Vedran Glisic, Apr 08 2011

a(n) = floor(10^(n*(n+1)/2)*123456789/999999999) - 10^n*floor(10^(n*(n-1)/2)*123456789/999999999). - Néstor Jofré, Jun 03 2017

Mathematica

A007923[n_Integer] := Module[{result = 0}, Do[ result += (Mod[(n*(n - 1)/2 + i - 1), 9] + 1) * 10^(n - i), {i, 1, n}   ]; result ]; Table[A007923[n], {n, 18}] (* James C. McMahon, Dec 04 2023 *)

Prog

(PARI) a(n)=my(m=(n*(n+1)/2-1)%9); sum(k=0, n-1, 10^k*((m-k)%9+1))

Crossrefs

Cf. A001369, A007924, A050234, A066547.

Sequence in context: A062273 A066547 A001369 * A080479 A053067 A036906

Adjacent sequences: A007920 A007921 A007922 * A007924 A007925 A007926

Keyword

nonn,easy,base

Author

R. Muller

Status

approved