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

1,2

Links

Table of n, a(n) for n=1..47.

Index entries for sequences related to the Josephus Problem

Formula

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

Example

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.

Mathematica

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

Prog

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

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.

Sequence in context: A136057 A177092 A023224 * A003215 A308685 A133323

Adjacent sequences: A113740 A113741 A113742 * A113744 A113745 A113746

Keyword

nonn

Author

Paul D. Hanna, Oct 12 2005

Extensions

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

Status

approved