A322431 Numbers k such that the coefficient of x^k in the expansion of Product_{j>=1} (1-x^j)^10 is zero.

6, 13, 17, 27, 28, 34, 36, 39, 41, 48, 55, 59, 61, 62, 72, 74, 76, 82, 83, 90, 93, 94, 97, 104, 105, 111, 112, 116, 121, 125, 127, 128, 131, 132, 138, 139, 146, 149, 151, 152, 153, 160, 168, 169, 174, 181, 182, 183, 188, 193, 195, 197, 202, 204, 207, 209, 211, 214, 215

Offset: 1

Author

Seiichi Manyama, Dec 07 2018

Keywords

• nonn

Comments

Indices of zero entries in A010818.

Also: numbers k such that 24k + 10 cannot be written as (12m+3)^2 + (4n+1)^2 with integers m, n. In this case, 12k + 5 is never prime. - M. F. Hasler, Jun 30 2025

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Numbers k such that the coefficient of x^k in the expansion of Product_{j>=1} (1 - x^j)^m is zero: A090864 (m=1), A213250 (m=2), A014132 (m=3), A302056 (m=4), A302057 (m=5), A020757 (m=6), A322430 (m=8), this sequence (m=10), A322432 (m=14), A322043 (m=15), A322433 (m=26).

Programs

PARI

my(x='x+O('x^300)); Vec(select(x->(x==0), Vec(eta(x)^10 - 1), 1)) \\ Michel Marcus, Dec 08 2018