A305553 Numbers that are not the sum of 2 squares and a 4th power.

7, 12, 15, 22, 23, 28, 31, 39, 43, 44, 47, 55, 60, 63, 67, 70, 71, 76, 78, 79, 87, 92, 93, 95, 103, 108, 111, 112, 119, 124, 127, 135, 140, 143, 151, 156, 159, 167, 168, 172, 175, 177, 183, 184, 188, 191, 192, 199, 204, 207, 214, 215, 220, 223, 231, 236

Offset: 1

Author

XU Pingya, Jun 20 2018

Keywords

• nonn

Comments

Numbers of the form 4*A017101(k) are terms of this sequence.

m is a term iff 16m is also.

Links

• W. Jagy and I. Kaplansky, Sums of Squares, Cubes and Higher Powers, Experimental Mathematics, vol. 4 (1995) pp. 169-173.

Crossrefs

Subsequence of A000037, A140823 and A022544.

A004215 and A214891 are subsequences.

Cf. A017101, A022552.

Programs

Mathematica

n=239;
t=Union@Flatten@Table[x^2+y^2+z^4, {x,0,n^(1/2)}, {y,x,(n-x^2)^(1/2)}, {z,0,(n-x^2-y^2)^(1/4)}];
Complement[Range[0,n], t]