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A121411
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Positive integers k for which there are primes of the form a^2+k^n=b^2+k^m with positive integers (a,b,m,n) and a > b.
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0
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2, 5, 6, 8, 10, 12, 13, 17, 18, 20, 21, 22, 26, 28, 30, 32, 33, 37, 38, 40, 42, 45, 46, 48, 50, 52, 53, 56, 58, 60, 61, 62, 65, 66, 68, 70, 72, 76, 77, 78, 80, 82, 85, 86, 88, 90, 92, 93, 96, 97, 98
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OFFSET
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1,1
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COMMENTS
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The sequence is "hard" in the sense that it not known how to prove that the necessary conditions are sufficient for the existence of primes.
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LINKS
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Table of n, a(n) for n=1..51.
David Broadhurst and Mike Oakes, Primes of the form a^2 + k^n = b^2 + k^m.
David Broadhurst and Mike Oakes, proof of the necessity the conditions given for the conjectured generating method.
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FORMULA
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Conjecturally, a(n) is the n-th positive nonsquare integer that is not congruent to -1 mod 4, nor to -1 mod 5, nor to -7 mod 16.
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EXAMPLE
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a(5455)=9998 because it was possible to find primes of the form a^2 + k^n = b^2 + k^m with positive integers (a,b,k,m,n), a > b, k < 10^4 and k satisfying the proved necessary conditions of the conjectured generating method.
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PROG
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(PARI) {ls=[]; for(k=1, 10^4, if(!issquare(k)&&(k+1)%4&&(k+1)%5&&(k+7)%16, ls=concat(ls, k))); print(ls)}
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CROSSREFS
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Sequence in context: A087943 A034020 A187476 * A224889 A047441 A284777
Adjacent sequences: A121408 A121409 A121410 * A121412 A121413 A121414
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KEYWORD
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hard,nonn
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AUTHOR
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David Broadhurst, Jul 29 2006
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STATUS
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approved
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