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A128292 Primes not in A126769. 4
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..51.

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

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Last modified January 17 09:54 EST 2020. Contains 330949 sequences. (Running on oeis4.)