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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 (list; graph; refs; listen; history; text; internal format)
 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 A047441 A284777 Adjacent sequences: A121408 A121409 A121410 * A121412 A121413 A121414 KEYWORD hard,nonn AUTHOR David Broadhurst, Jul 29 2006 STATUS approved

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Last modified March 23 10:25 EDT 2023. Contains 361443 sequences. (Running on oeis4.)