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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.

%I A112558 #12 Sep 30 2022 05:55:40
%S A112558 1,5,13,25,39,61,79,103,133,169,207,241,289,331,387,447,481,553,613,
%T A112558 687,763,819,927,979,1093,1179,1261,1347,1471,1539,1693,1759,1899,
%U A112558 2019,2161,2263,2367,2527,2703,2779,2967,3073,3199,3373,3529,3691,3841,3987,4203
%N 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.
%H A112558 <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>
%F A112558 a(2*n-1) = A000960(3*n-2), where A000960 is Flavius Josephus's sieve.
%e A112558 a(1)=1: 1;
%e A112558 a(2)=5: 2->5;
%e A112558 a(3)=13: 3->10->13;
%e A112558 a(4)=25: 4->15->22->25;
%e A112558 a(5)=39: 5->20->30->36->39;
%e A112558 a(6)=61: 6->25->40->51->58->61;
%e A112558 a(7)=79: 7->30->45->60->69->76->79;
%e A112558 a(8)=103: 8->35->54->70->84->93->100->103;
%e A112558 a(9)=133: 9->40->63->84->100->112->123->130->133;
%e A112558 a(10)=169: 10->45->72->98->120->135->148->159->166->169.
%t A112558 f[n_] := Fold[#2*Ceiling[#1/#2 + 3] &, n, Reverse@ Range[n - 1]]; Array[f, 49]
%o A112558 (PARI) a(n)=local(A=n,D);for(i=1,n-1,D=n-i;A=D*ceil(A/D+3));A
%Y A112558 Cf. A000012, A002491, A000960 (Flavius Josephus's sieve), A112557, A113742, A113743, A113744, A113745, A113746, A113747, A113748; A113749.
%K A112558 nonn
%O A112558 1,2
%A A112558 _Paul D. Hanna_, Oct 12 2005