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A128292 Primes not in A126769.

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%I A128292 #10 Jan 20 2020 12:41:09
%S A128292 2,3,5,7,11,13,37,47,61,67,97,107,127,137,157,167,197,227,233,317,331,
%T A128292 373,449,457,487,541,601,617,677,971,977,1153,1381,1447,1549,1637,
%U A128292 1777,1871,1931,1997,2287,2399,2417,2437,2647,2767,2777,2963,3089,3169,3187
%N A128292 Primes not in A126769.
%C A128292 Primes p that are not of the form k^4+s where k > 1 and s >= 1, such that k^2+s is prime and smaller than p.
%H A128292 Ray Chandler, <a href="/A128292/b128292.txt">Table of n, a(n) for n = 1..231</a> (computed from A126769 b-file)
%e A128292 37 is prime, 2^4+21 is the only way to write 37 as k^4+s, but neither 2^2+21 = 25 nor 3^2+21 = 30 is prime, hence 37 is a term.
%o A128292 (PARI) {m=8;v=[];for(n=2,m,for(k=1,(m+1)^4,if(isprime(p=n^4+k)&&p<m^4&&(q=n^2+k)<p&&isprime(q),v=concat(v,p))));v=Set(v);p=2;j=1;while(j<=#v&&p<=v[#v]&&v[j]<=m^4,if(p<v[j],print1(p,","),j++);p=nextprime(p+1))} \\ _Klaus Brockhaus_, Feb 24 2007
%o A128292 (PARI) findTerms(UpTo)={my(belongs,q,k,L:list=List());forprime(p=2,UpTo,belongs=0;for(s=1,p,if(ispower(p-s,4,&k),if(k>1,if(ispseudoprime(q=k^2+s),belongs=1;break))));if(!belongs,listput(L,p)));return(Vec(L))} \\ _R. J. Cano_, Apr 04 2018
%Y A128292 Cf. A126769.
%K A128292 nonn
%O A128292 1,1
%A A128292 _Klaus Brockhaus_, Feb 24 2007