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

0,2

Links

Table of n, a(n) for n=0..44.

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).

Prog

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

Crossrefs

Cf. A001316, A048883, A102376.

Sequence in context: A219797 A255744 A165831 * A286507 A286508 A287134

Adjacent sequences: A102374 A102375 A102376 * A102378 A102379 A102380

Keyword

easy,base,nonn

Author

Paul Barry, Jan 05 2005

Status

approved