A180018 Difference of sums of digits of n in decimal and in binary representation.

0, 0, 1, 1, 3, 3, 4, 4, 7, 7, -1, -1, 1, 1, 2, 2, 6, 6, 7, 7, 0, 0, 1, 1, 4, 4, 5, 5, 7, 7, -1, -1, 4, 4, 5, 5, 7, 7, 8, 8, 2, 2, 3, 3, 5, 5, 6, 6, 10, 10, 2, 2, 4, 4, 5, 5, 8, 8, 9, 9, 2, 2, 3, 3, 9, 9, 10, 10, 12, 12, 4, 4, 7, 7, 8, 8, 10, 10, 11, 11, 6, 6, 7, 7, 9, 9, 10, 10, 13, 13, 5, 5, 7, 7, 8, 8

Offset: 0

Author

Reinhard Zumkeller, Aug 06 2010

Keywords

• base
• sign

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Index entries for Colombian or self numbers and related sequences

Crossrefs

Cf. A180017, A180019, A007088.

Cf. A007953, A000120, A037308, A011557.

Cf. A000079, A002283, A008591, A000225.

Programs

Mathematica

Table[Total[IntegerDigits[n]]-Total[IntegerDigits[n,2]],{n,0,100}] (* Harvey P. Dale, Dec 27 2015 *)

PARI

a(n) = sumdigits(n) - hammingweight(n); \\ Michel Marcus, Nov 06 2022

Formula

a(n) = A007953(n) - A000120(n);

a(A037308(n)) = 0;

a(A011557(n)) = 1 - A000120(A011557(n));

a(A000079(n)) = A007953(A000079(n)) - 1;

a(A002283(n)) = A008591(n) - A000120(A002283(n));

a(A000225(n)) = A007953(A000225(n)) - n.