A145523 -id:A145523 - cp's OEIS frontend

A046641 a(n) is the smallest positive integer m such that the number of partitions p(m) = A000041(m) is divisible by n.

1, 2, 3, 11, 4, 9, 5, 11, 14, 9, 6, 21, 28, 10, 7, 15, 54, 21, 20, 58, 10, 8, 32, 21, 24, 28, 14, 11, 26, 9, 44, 66, 16, 94, 18, 21, 86, 47, 129, 66, 35, 10, 27, 15, 14, 75, 56, 70, 19, 74, 178, 62, 52, 340, 18, 11, 20, 26, 54, 124, 115, 101, 24, 66, 84, 21, 47, 94, 32, 19

Offset: 1

David W. Wilson

nonn

The initial term could also be taken to be 0.

From the formula a(p(n)) = n, it follows that every positive integer appears in this sequence. - Franklin T. Adams-Watters, Feb 09 2016

			The first partition number divisible by 9 is p(14) = 135, so a(9) = 14.

M. F. Hasler, Table of n, a(n) for n = 1..20000.
M. F. Hasler, A046641.c - C program for fast computation of a(n) for large values of n. [From _M. F. Hasler_, Oct 18 2008]

Cf. A000041, A040051.

See A091690 for simple PARI code, A145523(n)=a(2^n), A145524(n)=a(10^n), A145771 for record values. [M. F. Hasler, Oct 18 2008]

Table[SelectFirst[Range[10^3], Divisible[PartitionsP@ #, n] &], {n, 70}] (* Michael De Vlieger, Feb 10 2016, Version 10 *)

a(n) = my(m = 1); while(numbpart(m) % n, m++); m; \\ Michel Marcus, Feb 10 2016

a(p(n)) = n. - Franklin T. Adams-Watters, Feb 09 2016

Definition corrected by Max Alekseyev, Apr 25 2010

A145524 Least integer k>0 such that A000041(k) is divisible by 10^n.

Original entry on oeis.org

1, 9, 74, 449, 599, 11224, 55374, 3099324, 3099324

Offset: 0

M. F. Hasler, Oct 12 2008

The requirement a(n)>0 is somewhat arbitrary, chosen for agreement with A046641 ; a(n)>=0 would have been possible, too, yielding a(0)=0.

a(9) > 10^7. [From Max Alekseyev, Oct 18 2008]

Cf. A000041, A046641, A145523

a(n) = A046641(10^n)

a(6)..a(8) from Max Alekseyev, Oct 18 2008

cp's OEIS Frontend

A046641 a(n) is the smallest positive integer m such that the number of partitions p(m) = A000041(m) is divisible by n.

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