A344511 a(n) = Sum_{k >= 0} sign(d_k) * 2^k for any number n with decimal expansion Sum_{k >= 0} d_k * 10^k.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3

Offset: 0

Author

Rémy Sigrist, May 21 2021

Keywords

• nonn
• base

Comments

The binary expansion of a(n) encodes the nonzero digits of the decimal expansion of n.

Examples

			For n = 20!:
- 2432902008176640000 is the decimal expansion of 20!, so
  1111101001111110000 is the binary expansion of a(20!),
- a(20!) = 513008.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8191

Crossrefs

Cf. A007088, A140900, A289831 (base-3 analog), A343452.

Programs

PARI

a(n) = fromdigits(apply(sign, digits(n)), 2)

Python

def a(n): return int("".join((('1' if d!='0' else '0') for d in str(n))), 2)
print([a(n) for n in range(87)]) # Michael S. Branicky, May 22 2021

Formula

a(n) belongs to A140900 iff n belongs to A343452.

a(A007088(n)) = n.