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)
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
KEYWORD
AUTHOR
Yusuf Gurtas, Oct 29 2019
EXTENSIONS
More terms from Michel Marcus, Oct 30 2019
STATUS
approved