A079031 Least k > n such that p(n) divides p(k), where p(k) denotes the k-th partition number (A000041).

1, 2, 8, 7, 7, 10, 8, 9, 15, 97, 26, 75, 16, 356, 39, 96, 39, 39, 39, 264, 470, 776, 97, 711, 249, 765, 4458, 334, 699, 1084, 18911, 7150, 1447, 4604, 1399, 446, 36041, 5836, 3504, 1449, 4359, 6034, 688, 60818, 4514, 90825, 34641, 36852, 77173, 11100, 2564

Offset: 0

Author

Benoit Cloitre, Feb 01 2003

Keywords

• nonn

Comments

A000041(a(n)) mod A000041(n) = 0. - Reinhard Zumkeller, Aug 22 2003

Examples

			a(19)=264: A000041(264) = 670448123060170 = 2*5*(7^2)*13*41*1907*1346143 = (13*41*1907*1346143)*(2*5*7^2) = 1368261475633*490 = 1368261475633*A000041(19).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..72

Crossrefs

Cf. A000041.

Programs

Mathematica

Do[m = PartitionsP[n]; k = n + 1; While[Mod[PartitionsP[k], m] > 0, k++ ]; Print[k], {n, 0, 50}] (* Ryan Propper, Oct 31 2005 *)

PARI

a(n) = my(k=n+1, p=numbpart(n)); while (numbpart(k) % p, k++); k; \\ Michel Marcus, May 15 2020

Extensions

More terms from Reinhard Zumkeller, Aug 22 2003

Further terms from Ryan Propper, Oct 31 2005

a(0) inserted by Amiram Eldar, May 15 2020