A112565 Main diagonal of square table A112564 of generalized Flavius Josephus sieves.

1, 2, 7, 28, 125, 546, 2527, 11096, 43633, 186130, 809831, 3423432, 14022373, 58574894, 250708291, 1038612976, 4353755777, 18333324162, 74663736859, 311293807040, 1286700247561, 4917768055222, 20458840039199, 83985256000824

Offset: 0

Author

Paul D. Hanna, Oct 14 2005

Keywords

• nonn

Comments

Appears to be a self-convolution of an integer sequence (A112567).

Links

• Index entries for sequences related to the Josephus Problem

Crossrefs

Cf. A112564, A112566, A112567, A112568.

Programs

PARI

{a(n)=local(A=n,B=0,C=0);if(n==0,1, until(A==B,C=C+1;if(C%n==0,C=C+1);B=A;A=floor(A*(C+1)/C));1+A)}

PARI

A002491(n) = local(a, b); a = n; b = n - 1; while (b > 1, a = b*ceil(a/b); b--); a;
T(n, k) = local(A = k, C = 1, q, d, x); if (n*k == 0, return(1)); if (n == 1, return(A002491(k + 1))); while (q = A\C, d = A%C; x = d\q + 1; A += x*(n - 1)*(A\C); C += x*n); 1 + A; \\ David Wasserman, Jun 25 2009

Formula

a(n) = 1 + n*A112566(n) for n >= 0.

Extensions

More terms from David Wasserman, Jun 25 2009