A328882 a(n) = n - 2^(sum of digits of n).

-1, -1, -2, -5, -12, -27, -58, -121, -248, -503, 8, 7, 4, -3, -18, -49, -112, -239, -494, -1005, 16, 13, 6, -9, -40, -103, -230, -485, -996, -2019, 22, 15, 0, -31, -94, -221, -476, -987, -2010, -4057, 24, 9, -22, -85, -212, -467, -978, -2001, -4048, -8143, 18, -13, -76, -203, -458, -969, -1992, -4039, -8134, -16325, -4

Offset: 0

Author

Yusuf Gurtas, Oct 29 2019

Keywords

• sign
• base
• look

Comments

This sequence is a map from the set of nonnegative integers into the set of all integers. It is clearly not one-to-one. It is not known if it is onto.

Comments from N. J. A. Sloane, Nov 17 2019: (Start)

For m >= 0, A329002 gives an expression for the first time that m appears in this sequence (if it does appear), and A329492 plays a similar role for negative m.

In all these sequences it is safer to say "sum of digits" (which is A007953) rather than "digital sum" (which is also A007953), because many people confuse the latter term with the "digital root" (A010888). (End)

Examples

			a(0) = 0 - 2^0 = -1.
a(11) = 11 - 2^(1+1) = 7.
a(32) = 32 - 2^(3+2) = 0. The next time 0 occurs is at a(1180591620717411303424) = 1180591620717411303424 - 2^(70)=0.
The only known occurrence of 1 is when n=513: a(513) = 513 - 2^(5+1+3) = 1.
Smallest n such that a(n) = k, from _N. J. A. Sloane_, Nov 16 2019:
k = 0    1       2     3  4   5  6  7  8  9  10 ...
n = 32 513 2^103+2  1027 12 133 22 11 10 41 522 ...
k = -1 -2 -3 -4 -5   -6      -7  -8 -9     -10 11 ...
n =  0  2 13 60  3 1018 2^103-7 504 23 2^18-10  ? ...
		

Links

• N. J. A. Sloane, Table of n, a(n) for n = 0..9999

Crossrefs

Cf. A007953 (sum of digits of n), A329002, A329492, A329493.

Cf. also A007953, A010888.

Programs

Mathematica

Array[# - 2^Total[IntegerDigits@ #] &, 61, 0] (* Michael De Vlieger, Oct 30 2019 *)

PARI

a(n) = n - 2^sumdigits(n); \\ Michel Marcus, Oct 30 2019

Formula

a(n) = n - 2^A007953(n).

Extensions

More terms from Michel Marcus, Oct 30 2019