A303376 Numbers of the form a^6 + b^7, with integers a, b > 0.

2, 65, 129, 192, 730, 857, 2188, 2251, 2916, 4097, 4224, 6283, 15626, 15753, 16385, 16448, 17113, 17812, 20480, 32009, 46657, 46784, 48843, 63040, 78126, 78189, 78854, 82221, 93750, 117650, 117777, 119836, 124781, 134033, 195774, 262145, 262272, 264331, 278528, 279937

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..40.

Example

The sequence starts with 1^6 + 1^7, 2^6 + 1^7, 1^6 + 2^7, 2^6 + 2^7, 3^6 + 1^7, 3^6 + 2^7, ...

Mathematica

With[{nn=40}, Take[Union[First[#]^6 + Last[#]^7&/@Tuples[Range[nn], 2]], nn]] (* Vincenzo Librandi, Apr 25 2018 *)

Prog

(PARI) is(n, k=6, m=7)=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.
A303376_vec(L=10^5, k=6, m=7, 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).

Sequence in context: A229815 A273498 A003358 * A041511 A156651 A342608

Adjacent sequences: A303373 A303374 A303375 * A303377 A303378 A303379

Keyword

nonn,easy

Author

M. F. Hasler, Apr 22 2018

Status

approved