A115174 Numbers that are not the sum of a square, a nonnegative cube and a power of 2.

15, 22, 23, 55, 62, 87, 94, 106, 111, 118, 119, 120, 139, 167, 183, 188, 194, 195, 211, 215, 223, 244, 246, 251, 263, 274, 275, 279, 286, 303, 304, 307, 309, 311, 314, 330, 331, 335, 342, 343, 350, 398, 399, 419, 421, 434, 436, 437, 438, 454, 455, 461, 463

Offset: 1

Author

Giovanni Resta, Jan 15 2006

Keywords

• nonn

Comments

The square and the cube may be equal to 0, the powers of two starts at 2^0 = 1.

There are 531362099 such numbers up to 10^9, the last one in this range being 999999999.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A115171, A115172, A115173, A115175, A115176, A115177.

Programs

Maple

N:= 1000: # for terms <= N
S1:= {seq(i^2,i=0..isqrt(N))}:
S2:= {seq(i^3,i=0..floor(N^(1/3)))}:
S3:= {seq(2^i,i=0..ilog2(N))}:
S:= select(`<=`,{seq(seq(seq(a+b+c,a=S1),b=S2),c=S3)},N):
sort(convert({$1..N} minus S,list)); # Robert Israel, Jul 23 2020

Mathematica

Complement[Range[1000], Plus @@@ Tuples[{Range[0, 34]^2, Range[0, 10]^3, 2^Range[0, 9]}]] (* Giovanni Resta, May 02 2016 *)

Extensions

Name corrected by Giovanni Resta, May 02 2016