A102377 Gould's sequence A001316 in binary.

1, 10, 10, 100, 10, 100, 100, 1000, 10, 100, 100, 1000, 100, 1000, 1000, 10000, 10, 100, 100, 1000, 100, 1000, 1000, 10000, 100, 1000, 1000, 10000, 1000, 10000, 10000, 100000, 10, 100, 100, 1000, 100, 1000, 1000, 10000, 100, 1000, 1000, 10000, 1000

Offset: 0

Author

Paul Barry, Jan 05 2005

Keywords

• easy
• base
• nonn

Crossrefs

Cf. A001316, A048883, A102376.

Programs

PARI

a(n) = 10^hammingweight(n); \\ Kevin Ryde, Jan 11 2024

Formula

Formulas due to Paul D. Hanna:

a(n) = 10^A000120(n).

a(n) = Product_{k=0..log_2(n)} 10^b(n,k) where b(n,k) = coefficient of 2^k in binary expansion of n.

a(n) = Sum_{k=0..n} (C(n,k) mod 2)*9^A000120(n-k).

G.f.: Product_{k>=0} 1 + 10*x^(2^k).