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A303372
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Numbers of the form a^2 + b^6, with integers a, b > 0.
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8
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2, 5, 10, 17, 26, 37, 50, 65, 68, 73, 80, 82, 89, 100, 101, 113, 122, 128, 145, 164, 170, 185, 197, 208, 226, 233, 257, 260, 289, 290, 320, 325, 353, 362, 388, 401, 425, 442, 464, 485, 505, 530, 548, 577, 593, 626, 640, 677, 689, 730, 733, 738, 740, 745, 754, 765, 778
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listen;
history;
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OFFSET
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1,1
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COMMENTS
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A subsequence of A055394, the numbers of the form a^2 + b^3.
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.
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LINKS
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EXAMPLE
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The first terms are 1^2 + 1^6 = 2, 2^2 + 1^6 = 5, 3^2 + 1^6 = 10, 4^2 + 1^6 = 17, 5^2 + 1^6 = 26, ..., 8^2 + 1^6 = 1^2 + 2^6 = 65, 2^2 + 2^6 = 68, 3^2 + 2^6 = 73, ...
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PROG
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(PARI) is(n, k=2, 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.
A303372_vec(L=10^5, k=2, 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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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