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

1,1

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.

Links

Table of n, a(n) for n=1..57.

Example

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, ...

Prog

(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

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).

Sequence in context: A078325 A059591 A082607 * A159547 A002522 A217990

Adjacent sequences: A303369 A303370 A303371 * A303373 A303374 A303375

Keyword

nonn,easy

Author

M. F. Hasler, Apr 22 2018

Status

approved