A112564 Square array, read by ascending antidiagonals, where each row is a generalized Flavius Josephus sieve (A000960).

1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 7, 6, 1, 1, 5, 13, 13, 10, 1, 1, 6, 21, 28, 19, 12, 1, 1, 7, 31, 61, 61, 27, 18, 1, 1, 8, 43, 96, 125, 88, 39, 22, 1, 1, 9, 57, 169, 241, 261, 133, 49, 30, 1, 1, 10, 73, 232, 505, 546, 421, 208, 63, 34, 1, 1, 11, 91, 361, 785, 1051, 1171, 605, 313

Offset: 0

Author

Paul D. Hanna, Oct 14 2005

Keywords

• nonn
• tabl

Examples

			Table begins:
  1,  1,  1,   1,    1,    1,     1,     1,      1,     1, ...
  1,  2,  4,   6,   10,   12,    18,    22,     30,    34, ...
  1,  3,  7,  13,   19,   27,    39,    49,     63,    79, ...
  1,  4, 13,  28,   61,   88,   133,   208,    313,   364, ...
  1,  5, 21,  61,  125,  261,   421,   605,   1101,  1681, ...
  1,  6, 31,  96,  241,  546,  1171,  1776,   2761,  5046, ...
  1,  7, 43, 169,  505, 1051,  2527,  5083,  7729,  11635, ...
  1,  8, 57, 232,  785, 1800,  5041, 11096, 22737,  34504, ...
  1,  9, 73, 361, 1153, 3961,  8281, 20161, 43633,  95049, ...
  1, 10, 91, 460, 1981, 5950, 13951, 38080, 91081, 186130, ...
  ...
		

Links

• Index entries for sequences related to the Josephus Problem

Crossrefs

Cf. A002491 (row 1), A000960 (row 2), A112560 (row 3), A112561 (row 4), A112562 (row 5), A112563 (row 6), A112565 (main diagonal), A112568 (2nd diagonal), A112569 (antidiagonal sums).

Programs

PARI

{T(n,k)=local(A=k,B=0,C=0);if(n==0||k==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)}