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

0,3

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)

Links

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

Formula

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

Example

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  ? ...

Mathematica

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

Prog

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

Crossrefs

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

Cf. also A007953, A010888.

Sequence in context: A111000 A362195 A362196 * A362197 A000325 A076878

Adjacent sequences: A328879 A328880 A328881 * A328883 A328884 A328885

Keyword

sign,base,look

Author

Yusuf Gurtas, Oct 29 2019

Extensions

More terms from Michel Marcus, Oct 30 2019

Status

approved