A303372 Numbers of the form a^2 + b^6, with integers a, b > 0.

2, 5, 10, 17, 26, 37, 50, 65, 68, 73, 80, 82, 89, 100, 101, 113, 122, 128, 145, 164, 170, 185, 197, 208, 226, 233, 257, 260, 289, 290, 320, 325, 353, 362, 388, 401, 425, 442, 464, 485, 505, 530, 548, 577, 593, 626, 640, 677, 689, 730, 733, 738, 740, 745, 754, 765, 778

Offset: 1

Author

M. F. Hasler, Apr 22 2018

Keywords

• nonn
• easy

Comments

A subsequence of A055394, the numbers of the form a^2 + b^3.

Although it is easy to produce many terms of this sequence, it is nontrivial to check whether a very large number is of this form.

Examples

			The first terms are 1^2 + 1^6 = 2, 2^2 + 1^6 = 5, 3^2 + 1^6 = 10, 4^2 + 1^6 = 17, 5^2 + 1^6 = 26, ..., 8^2 + 1^6 = 1^2 + 2^6 = 65, 2^2 + 2^6 = 68, 3^2 + 2^6 = 73, ...
		

Crossrefs

Cf. A055394 (a^2 + b^3), A111925 (a^2 + b^4), A100291 (a^4 + b^3), A100292 (a^5 + b^2), A100293 (a^5 + b^3), A100294 (a^5 + b^4).

Cf. A303373 (a^3 + b^6), A303374 (a^4 + b^6), A303375 (a^5 + b^6).

Programs

PARI

is(n,k=2,m=6)=for(b=1,sqrtnint(n-1,m),ispower(n-b^m,k)&&return(b)) \\ Returns b > 0 if n is in the sequence, else 0.
A303372_vec(L=10^5,k=2,m=6,S=List())={for(a=1,sqrtnint(L-1,m),for(b=1,sqrtnint(L-a^m,k),listput(S,a^m+b^k)));Set(S)} \\ List of all terms up to limit L