A374446 Positions of zeros in the expansion of Product_{k>=0} (1 - x^(2^k))^3; A373308(a(n)) = 0 for n >= 1.

2, 11, 14, 47, 50, 59, 62, 191, 194, 203, 206, 239, 242, 251, 254, 767, 770, 779, 782, 815, 818, 827, 830, 959, 962, 971, 974, 1007, 1010, 1019, 1022, 3071, 3074, 3083, 3086, 3119, 3122, 3131, 3134, 3263, 3266, 3275, 3278, 3311, 3314, 3323, 3326, 3839, 3842, 3851, 3854, 3887, 3890, 3899

Offset: 1

Author

Paul D. Hanna, Jul 08 2024

Keywords

• nonn

Comments

Conjecture: a(n) = A001196(n) - 1 for n >= 1, where A001196 lists numbers with only even length runs in their binary expansion.

Examples

			Product_{k>=0} (1 - x^(2^k))^3 = 1 - 3*x + 0*x^2 + 8*x^3 - 9*x^4 + 3*x^5 + 8*x^6 - 24*x^7 + 15*x^8 + 19*x^9 - 24*x^10 + 0*x^11 + 17*x^12 - 27*x^13 + 0*x^14 + 64*x^15 + ... + A373308(n)*x^n + ...
in which the coefficients of {x^2, x^11, x^14, x^47, ..., x^a(n), ...} are zero.
Compare to numbers with only even length runs in their binary expansion: A001196 = [3, 12, 15, 48, 51, 60, 63, 192, 195, 204, 207, 240, 243, 252, 255, 768, ...]; it appears that a(n) = A001196(n) - 1 for n >= 1.
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 1..511

Crossrefs

Cf. A001196, A000695, A373308.