A303377 Numbers of the form a^7 + b^8, with integers a, b > 0.

2, 129, 257, 384, 2188, 2443, 6562, 6689, 8748, 16385, 16640, 22945, 65537, 65664, 67723, 78126, 78381, 81920, 84686, 143661, 279937, 280192, 286497, 345472, 390626, 390753, 392812, 407009, 468750, 670561, 823544, 823799, 830104, 889079, 1214168, 1679617, 1679744, 1681803

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..38.

Example

The sequence starts with 1^7 + 1^8, 2^7 + 1^8, 1^7 + 2^8, 2^7 + 2^8, 3^7 + 1^8, 3^7 + 2^8, 1^7 + 3^8, 2^7 + 3^8, 3^7 + 3^8, 4^7 + 1^8, 4^7 + 2^8, 4^7 + 3^8, 1, ...

Mathematica

With[{nn=40}, Take[Union[First[#]^7 + Last[#]^8&/@Tuples[Range[nn], 2]], nn]]

Prog

(PARI) is(n, k=7, m=8)=for(b=1, sqrtnint(n-1, m), ispower(n-b^m, n)&&return(b)) \\ Returns b > 0 if n is in the sequence, else 0.
A303377_vec(L=10^7, k=7, m=8, 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)} \\ all terms up to limit L

Crossrefs

Cf. A000404 (a^2 + b^2), 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. A303372 (a^2 + b^6), A303373 (a^3 + b^6), A303374 (a^4 + b^6), A303375 (a^5 + b^6), A303376 (a^6 + b^7).

Sequence in context: A296060 A090121 A003369 * A342618 A258806 A216358

Adjacent sequences: A303374 A303375 A303376 * A303378 A303379 A303380

Keyword

nonn,easy

Author

M. F. Hasler, May 04 2018

Status

approved