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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.

%I A113743 #13 Jun 23 2020 19:10:25
%S A113743 1,7,19,37,61,87,123,163,207,253,307,373,447,511,589,673,763,843,949,
%T A113743 1087,1179,1309,1393,1531,1693,1807,1933,2119,2263,2439,2559,2761,
%U A113743 2967,3147,3327,3499,3691,3883,4123,4309,4603,4783,5067,5209,5539,5763,6013
%N 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.
%H A113743 <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>
%F A113743 a(4*n-3) = A112558(5*n-4), a(8*n-7) = A000960(15*n-14), for n>=1.
%e A113743 a(1)=1: 1;
%e A113743 a(2)=7: 2->7;
%e A113743 a(3)=19: 3->14->19;
%e A113743 a(4)=37: 4->21->32->37;
%e A113743 a(5)=61: 5->28->45->56->61;
%e A113743 a(6)=87: 6->35->56->72->82->87;
%e A113743 a(7)=123: 7->42->70->92->108->118->123;
%e A113743 a(8)=163: 8->49->84->110->132->147->158->163;
%e A113743 a(9)=207: 9->56->91->126->155->176->192->202->207;
%e A113743 a(10)=253: 10->63->104->140->174->200->220->237->248->253.
%t A113743 f[n_] := Fold[ #2*Ceiling[ #1/#2 + 5] &, n, Reverse@Range[n - 1]]; Array[f, 47]
%o A113743 (PARI) a(n)=local(A=n,D);for(i=1,n-1,D=n-i;A=D*ceil(A/D+5));A
%Y A113743 Cf. {k=-1..12} A000012, A002491, A000960 (Flavius Josephus's sieve), A112557, A112558, A113742, A113743, A113744, A113745, A113746, A113747, A113748; det. A113749.
%Y A113743 Cf. A002491, A000960, A112557, A112558.
%K A113743 nonn
%O A113743 1,2
%A A113743 _Paul D. Hanna_, Oct 12 2005
%E A113743 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, May 31 2007