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

0,5

Links

Table of n, a(n) for n=0..74.

Index entries for sequences related to the Josephus Problem

Example

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, ...
  ...

Prog

(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)}

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).

Sequence in context: A179743 A113749 A109225 * A244911 A258309 A197957

Adjacent sequences: A112561 A112562 A112563 * A112565 A112566 A112567

Keyword

nonn,tabl

Author

Paul D. Hanna, Oct 14 2005

Status

approved