cp's OEIS Frontend

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

%I A112565 #14 Oct 04 2024 16:37:59
%S A112565 1,2,7,28,125,546,2527,11096,43633,186130,809831,3423432,14022373,
%T A112565 58574894,250708291,1038612976,4353755777,18333324162,74663736859,
%U A112565 311293807040,1286700247561,4917768055222,20458840039199,83985256000824
%N A112565 Main diagonal of square table A112564 of generalized Flavius Josephus sieves.
%C A112565 Appears to be a self-convolution of an integer sequence (A112567).
%H A112565 <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>
%F A112565 a(n) = 1 + n*A112566(n) for n >= 0.
%o A112565 (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)}
%o A112565 (PARI) A002491(n) = local(a, b); a = n; b = n - 1; while (b > 1, a = b*ceil(a/b); b--); a;
%o A112565 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
%Y A112565 Cf. A112564, A112566, A112567, A112568.
%K A112565 nonn
%O A112565 0,2
%A A112565 _Paul D. Hanna_, Oct 14 2005
%E A112565 More terms from _David Wasserman_, Jun 25 2009