cp's OEIS Frontend

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

%I A328882 #70 Nov 12 2023 05:33:06
%S A328882 -1,-1,-2,-5,-12,-27,-58,-121,-248,-503,8,7,4,-3,-18,-49,-112,-239,
%T A328882 -494,-1005,16,13,6,-9,-40,-103,-230,-485,-996,-2019,22,15,0,-31,-94,
%U A328882 -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
%N A328882 a(n) = n - 2^(sum of digits of n).
%C A328882 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.
%C A328882 Comments from _N. J. A. Sloane_, Nov 17 2019: (Start)
%C A328882 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.
%C A328882 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)
%H A328882 N. J. A. Sloane, <a href="/A328882/b328882.txt">Table of n, a(n) for n = 0..9999</a>
%F A328882 a(n) = n - 2^A007953(n).
%e A328882 a(0) = 0 - 2^0 = -1.
%e A328882 a(11) = 11 - 2^(1+1) = 7.
%e A328882 a(32) = 32 - 2^(3+2) = 0. The next time 0 occurs is at a(1180591620717411303424) = 1180591620717411303424 - 2^(70)=0.
%e A328882 The only known occurrence of 1 is when n=513: a(513) = 513 - 2^(5+1+3) = 1.
%e A328882 Smallest n such that a(n) = k, from _N. J. A. Sloane_, Nov 16 2019:
%e A328882 k = 0    1       2     3  4   5  6  7  8  9  10 ...
%e A328882 n = 32 513 2^103+2  1027 12 133 22 11 10 41 522 ...
%e A328882 k = -1 -2 -3 -4 -5   -6      -7  -8 -9     -10 11 ...
%e A328882 n =  0  2 13 60  3 1018 2^103-7 504 23 2^18-10  ? ...
%t A328882 Array[# - 2^Total[IntegerDigits@ #] &, 61, 0] (* _Michael De Vlieger_, Oct 30 2019 *)
%o A328882 (PARI) a(n) = n - 2^sumdigits(n); \\ _Michel Marcus_, Oct 30 2019
%Y A328882 Cf. A007953 (sum of digits of n), A329002, A329492, A329493.
%Y A328882 Cf. also A007953, A010888.
%K A328882 sign,base,look
%O A328882 0,3
%A A328882 _Yusuf Gurtas_, Oct 29 2019
%E A328882 More terms from _Michel Marcus_, Oct 30 2019