A303376 - OEIS

%I #7 Apr 25 2018 14:01:21

%S 2,65,129,192,730,857,2188,2251,2916,4097,4224,6283,15626,15753,16385,

%T 16448,17113,17812,20480,32009,46657,46784,48843,63040,78126,78189,

%U 78854,82221,93750,117650,117777,119836,124781,134033,195774,262145,262272,264331,278528,279937

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

%C 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.

%e 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, ...

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

%o (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.

%o 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

%Y 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).

%Y Cf. A303372 (a^2 + b^6), A303373 (a^3 + b^6), A303374 (a^4 + b^6), A303375 (a^5 + b^6).

%K nonn,easy

%O 1,1

%A _M. F. Hasler_, Apr 22 2018