OFFSET
1,1
COMMENTS
A subsequence of A000404 (a^2 + b^2), A055394 (a^2 + b^3), A111925 (a^4 + b^2), A100291 (a^4 + b^3), A303372 (a^2 + b^6).
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. Maybe the most efficient way is to consider decompositions of n into sums of two positive squares (see sum2sqr in A133388), and check if one of the terms is a third power and the other a fourth power.
PROG
(PARI) is(n, k=4, 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.
is(n, L=sum2sqr(n))={for(i=1, #L, L[i][1]&&for(j=1, 2, ispower(L[i][j], 3)&&issquare(L[i][3-j])&&return(L[i][j])))} \\ See A133388 for sum2sqr(). Much faster than the above for n >> 10^30.
A303374(L=10^5, k=4, m=6, S=[])={for(a=1, sqrtnint(L-1, m), for(b=1, sqrtnint(L-a^m, k), S=setunion(S, [a^m+b^k]))); S}
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
M. F. Hasler, Apr 22 2018
STATUS
approved