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%I #2 Oct 01 2013 21:35:22
%S 1,4,9,10,25,35,36,46,49,64,66,75,113,144,149,179,188,196,203,221,241,
%T 250,290,302,380,395,397,400
%N 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.
%C 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.
%e p=7,q=11,k=4. 7*11+4 = 81 = 3^4.
%o (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) }
%Y Cf. A129783.
%K easy,nonn
%O 1,2
%A _Cino Hilliard_, May 21 2007
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