A344511 - OEIS

%I #13 May 24 2021 07:54:33

%S 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,

%T 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,

%U 3,3,2,3,3,3,3,3,3,3,3,3,2,3,3,3,3,3,3

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

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

%H Rémy Sigrist, <a href="/A344511/b344511.txt">Table of n, a(n) for n = 0..8191</a>

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

%F a(A007088(n)) = n.

%e For n = 20!:

%e - 2432902008176640000 is the decimal expansion of 20!, so

%e   1111101001111110000 is the binary expansion of a(20!),

%e - a(20!) = 513008.

%o (PARI) a(n) = fromdigits(apply(sign, digits(n)), 2)

%o (Python)

%o def a(n): return int("".join((('1' if d!='0' else '0') for d in str(n))), 2)

%o print([a(n) for n in range(87)]) # _Michael S. Branicky_, May 22 2021

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

%K nonn,base

%O 0,11

%A _Rémy Sigrist_, May 21 2021