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
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
Programs
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PARI
a(n) = fromdigits(apply(sign, digits(n)), 2)
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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
Comments