A113743 Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 6 multiples of n-1, n-2, ..., 1.

1, 7, 19, 37, 61, 87, 123, 163, 207, 253, 307, 373, 447, 511, 589, 673, 763, 843, 949, 1087, 1179, 1309, 1393, 1531, 1693, 1807, 1933, 2119, 2263, 2439, 2559, 2761, 2967, 3147, 3327, 3499, 3691, 3883, 4123, 4309, 4603, 4783, 5067, 5209, 5539, 5763, 6013

Offset: 1

Author

Paul D. Hanna, Oct 12 2005

Keywords

• nonn

Examples

			a(1)=1: 1;
a(2)=7: 2->7;
a(3)=19: 3->14->19;
a(4)=37: 4->21->32->37;
a(5)=61: 5->28->45->56->61;
a(6)=87: 6->35->56->72->82->87;
a(7)=123: 7->42->70->92->108->118->123;
a(8)=163: 8->49->84->110->132->147->158->163;
a(9)=207: 9->56->91->126->155->176->192->202->207;
a(10)=253: 10->63->104->140->174->200->220->237->248->253.
		

Links

• Index entries for sequences related to the Josephus Problem

Crossrefs

Cf. {k=-1..12} A000012, A002491, A000960 (Flavius Josephus's sieve), A112557, A112558, A113742, A113743, A113744, A113745, A113746, A113747, A113748; det. A113749.

Cf. A002491, A000960, A112557, A112558.

Programs

Mathematica

f[n_] := Fold[ #2*Ceiling[ #1/#2 + 5] &, n, Reverse@Range[n - 1]]; Array[f, 47]

PARI

a(n)=local(A=n,D);for(i=1,n-1,D=n-i;A=D*ceil(A/D+5));A

Formula

a(4*n-3) = A112558(5*n-4), a(8*n-7) = A000960(15*n-14), for n>=1.

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 31 2007