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A303375
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Numbers of the form a^5 + b^6, with integers a, b > 0.
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9
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2, 33, 65, 96, 244, 307, 730, 761, 972, 1025, 1088, 1753, 3126, 3189, 3854, 4097, 4128, 4339, 5120, 7221, 7777, 7840, 8505, 11872, 15626, 15657, 15868, 16649, 16808, 16871, 17536, 18750, 20903, 23401, 32432, 32769, 32832, 33497, 36864, 46657, 46688, 46899, 47680, 48393
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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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.
This sequence is among others motivated by the hard-to-compute sequence A300567 = numbers z such that z^7 = x^5 + y^6 for some x, y >= 1.
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LINKS
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Table of n, a(n) for n=1..44.
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PROG
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(PARI) is(n, k=5, m=6)=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.
A303375_vec(L=10^5, k=5, 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)} \\ all terms up to limit L
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CROSSREFS
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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).
See also A300567: numbers z such that z^7 = x^5 + y^6 for some x, y >= 1.
Sequence in context: A048783 A116340 A003347 * A342620 A065647 A041127
Adjacent sequences: A303372 A303373 A303374 * A303376 A303377 A303378
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KEYWORD
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nonn,easy
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AUTHOR
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M. F. Hasler, Apr 22 2018
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STATUS
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approved
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