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 A129830 Conjectured first occurrence of numbers n with the property that there exist two consecutive primes p and q such that pq + n is a fourth power. 0
 1, 4, 9, 10, 25, 35, 36, 46, 49, 64, 66, 75, 113, 144, 149, 179, 188, 196, 203, 221, 241, 250, 290, 302, 380, 395, 397, 400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS It remains to prove that for certain n, pq+n != y^4 for all consecutive primes p and q. This list was computed for p and q with prime indices up to 10000. LINKS EXAMPLE p=7,q=11,k=4. 7*11+4 = 81 = 3^4. PROG (PARI) primefourth(n, m) = { local(c, k, x, p1, p2, j); c=0; for(k=1, m, for(x=1, n, p1=prime(x); p2=(prime(x+1)); y=p1*p2+k; if(isfourth(y), c++; print1(k", "); break; ) ) ); c; } isfourth(n) = \Return 1 if n is a fourth power { local(r); r = sqrt(sqrt(n)); if(floor(r+.5)^4== n, 1, 0) } CROSSREFS Cf. A129783. Sequence in context: A093896 A191905 A113432 * A113434 A236024 A141395 Adjacent sequences:  A129827 A129828 A129829 * A129831 A129832 A129833 KEYWORD easy,nonn AUTHOR Cino Hilliard, May 21 2007 STATUS approved

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Last modified August 26 05:23 EDT 2019. Contains 326328 sequences. (Running on oeis4.)