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%I #10 Nov 22 2023 19:08:05
%S 0,8,9,10,16,18,32,58,129,5484,28158,55573,89570,371255,13877936
%N Indices of records in A091719 (greatest common divisors of consecutive partition numbers).
%C The corresponding record values are 1, 2, 6, 14, 33, 35, 69, 220, 17270, 19085, 64190, 471725, 1551362, 8215449, 8990167, ...
%e 8 is a term since partition(8) = 22 and partition(9) = 30, so A091719(8) = gcd(22, 30) = 2, while A091719(k) = 1 for all k < 8.
%t p1 = PartitionsP[0]; gm = 0; seq = {}; Do[p2 = PartitionsP[n]; g = GCD[p1, p2]; If[g > gm, gm = g; AppendTo[seq, n-1]]; p1 = p2, {n, 1, 10^4}]; seq
%t DeleteDuplicates[With[{nn=900000},Thread[{Range[nn],GCD@@#&/@Partition[PartitionsP[ Range[ 0,nn]],2,1]}]],GreaterEqual[#1[[2]],#2[[2]]]&][[;;,1]]-1 (* The program generates the first 13 terms of the sequence. *) (* _Harvey P. Dale_, Nov 22 2023 *)
%Y Cf. A000041, A091719.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, May 09 2020
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