A128292 Primes not in A126769.

2, 3, 5, 7, 11, 13, 37, 47, 61, 67, 97, 107, 127, 137, 157, 167, 197, 227, 233, 317, 331, 373, 449, 457, 487, 541, 601, 617, 677, 971, 977, 1153, 1381, 1447, 1549, 1637, 1777, 1871, 1931, 1997, 2287, 2399, 2417, 2437, 2647, 2767, 2777, 2963, 3089, 3169, 3187

Offset: 1

Author

Klaus Brockhaus, Feb 24 2007

Keywords

• nonn

Comments

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.

Examples

			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.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..231 (computed from A126769 b-file)

Crossrefs

Cf. A126769.

Programs

PARI

{m=8;v=[];for(n=2,m,for(k=1,(m+1)^4,if(isprime(p=n^4+k)&&pKlaus Brockhaus, Feb 24 2007

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