cp's OEIS Frontend

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.

%I A344511 #13 May 24 2021 07:54:33
%S A344511 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 A344511 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 A344511 3,3,2,3,3,3,3,3,3,3,3,3,2,3,3,3,3,3,3
%N 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.
%C A344511 The binary expansion of a(n) encodes the nonzero digits of the decimal expansion of n.
%H A344511 Rémy Sigrist, <a href="/A344511/b344511.txt">Table of n, a(n) for n = 0..8191</a>
%F A344511 a(n) belongs to A140900 iff n belongs to A343452.
%F A344511 a(A007088(n)) = n.
%e A344511 For n = 20!:
%e A344511 - 2432902008176640000 is the decimal expansion of 20!, so
%e A344511   1111101001111110000 is the binary expansion of a(20!),
%e A344511 - a(20!) = 513008.
%o A344511 (PARI) a(n) = fromdigits(apply(sign, digits(n)), 2)
%o A344511 (Python)
%o A344511 def a(n): return int("".join((('1' if d!='0' else '0') for d in str(n))), 2)
%o A344511 print([a(n) for n in range(87)]) # _Michael S. Branicky_, May 22 2021
%Y A344511 Cf. A007088, A140900, A289831 (base-3 analog), A343452.
%K A344511 nonn,base
%O A344511 0,11
%A A344511 _Rémy Sigrist_, May 21 2021