A334728 Indices of records in A091719 (greatest common divisors of consecutive partition numbers).

0, 8, 9, 10, 16, 18, 32, 58, 129, 5484, 28158, 55573, 89570, 371255, 13877936

Offset

1,2

Comments

The corresponding record values are 1, 2, 6, 14, 33, 35, 69, 220, 17270, 19085, 64190, 471725, 1551362, 8215449, 8990167, ...

Links

Table of n, a(n) for n=1..15.

Example

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.

Mathematica

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
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 *)

Crossrefs

Cf. A000041, A091719.

Sequence in context: A358675 A091417 A069237 * A070480 A135043 A054966

Adjacent sequences: A334725 A334726 A334727 * A334729 A334730 A334731

Keyword

nonn,more

Author

Amiram Eldar, May 09 2020

Status

approved