A112558 Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 4 multiples of n-1, n-2, ..., 1, for n>=1.

1, 5, 13, 25, 39, 61, 79, 103, 133, 169, 207, 241, 289, 331, 387, 447, 481, 553, 613, 687, 763, 819, 927, 979, 1093, 1179, 1261, 1347, 1471, 1539, 1693, 1759, 1899, 2019, 2161, 2263, 2367, 2527, 2703, 2779, 2967, 3073, 3199, 3373, 3529, 3691, 3841, 3987, 4203

Offset: 1

Author

Paul D. Hanna, Oct 12 2005

Keywords

• nonn

Examples

			a(1)=1: 1;
a(2)=5: 2->5;
a(3)=13: 3->10->13;
a(4)=25: 4->15->22->25;
a(5)=39: 5->20->30->36->39;
a(6)=61: 6->25->40->51->58->61;
a(7)=79: 7->30->45->60->69->76->79;
a(8)=103: 8->35->54->70->84->93->100->103;
a(9)=133: 9->40->63->84->100->112->123->130->133;
a(10)=169: 10->45->72->98->120->135->148->159->166->169.
		

Links

• Index entries for sequences related to the Josephus Problem

Crossrefs

Cf. A000012, A002491, A000960 (Flavius Josephus's sieve), A112557, A113742, A113743, A113744, A113745, A113746, A113747, A113748; A113749.

Programs

Mathematica

f[n_] := Fold[#2*Ceiling[#1/#2 + 3] &, n, Reverse@ Range[n - 1]]; Array[f, 49]

PARI

a(n)=local(A=n,D);for(i=1,n-1,D=n-i;A=D*ceil(A/D+3));A

Formula

a(2*n-1) = A000960(3*n-2), where A000960 is Flavius Josephus's sieve.