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

1,1

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.

Links

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

Example

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.

Prog

(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
(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

Crossrefs

Cf. A126769.

Sequence in context: A262377 A237600 A228199 * A140464 A037174 A238851

Adjacent sequences: A128289 A128290 A128291 * A128293 A128294 A128295

Keyword

nonn

Author

Klaus Brockhaus, Feb 24 2007

Status

approved