A303373 - OEIS

%I #10 Apr 23 2018 02:57:56

%S 2,9,28,65,72,91,126,128,189,217,280,344,407,513,576,730,737,756,793,

%T 854,945,1001,1064,1072,1241,1332,1395,1458,1729,1792,2060,2198,2261,

%U 2457,2745,2808,2926,3376,3439,3473,4097,4104,4123,4160,4221,4312,4439,4608,4825,4914

%N Numbers of the form a^3 + b^6, with integers a, b > 0.

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

%C 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.

%e The first terms are 1^3 + 1^6 = 2, 2^3 + 1^6 = 9, 3^3 + 1^6 = 28, 4^3 + 1^6 = 65, 2^3 + 2^6 = 72, 3^3 + 2^6 = 91, 5^3 + 1^6 = 126, 4^3 + 2^6 = 128, ...

%o (PARI) is(n,k=3,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.

%o A303373_vec(L=10^5,k=3,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

%Y 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).

%Y Cf. A303372 (a^2 + 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