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A121411
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.
0
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
OFFSET
1,1
COMMENTS
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.
LINKS
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.
FORMULA
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.
EXAMPLE
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.
PROG
(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)}
CROSSREFS
Sequence in context: A087943 A034020 A187476 * A224889 A363676 A047441
KEYWORD
hard,nonn
AUTHOR
David Broadhurst, Jul 29 2006
STATUS
approved