A216497 Primes p with property that there exists a number d>0 such that numbers p-k*d, k=1...4, are four primes.

29, 53, 127, 131, 157, 173, 197, 227, 251, 257, 271, 283, 293, 311, 353, 373, 389, 397, 421, 443, 449, 463, 479, 509, 521, 587, 607, 613, 617, 661, 673, 677, 691, 719, 757, 761, 811, 821, 823, 839, 853, 859, 863, 881, 887, 907, 911, 941, 953, 967, 983, 997, 1013

Offset

1,1

Comments

Conjecture: only 653 primes are not in the sequence: 2, 3, ..., 100291.

Links

Table of n, a(n) for n=1..53.

Example

29 is in the sequence because with d=6: 23, 17, 11, 5 are all primes.

Mathematica

prms = 4; fQ[p_] := Module[{d = 1}, While[prms*d < p && Union[PrimeQ[p - Range[prms]*d]] != {True}, d++]; prms*d < p]; Select[Prime[Range[2, PrimePi[1013]]], fQ] (* T. D. Noe, Sep 08 2012 *)

Prog

(PARI) is(n)=my(t); forprime(p=2, n-12, if((n-p)%4==0 && isprime((t=(n-p)/4)+p) && isprime(2*t+p) && isprime(3*t+p) && isprime(n), return(1))); 0 \\ Charles R Greathouse IV, Sep 10 2014

Crossrefs

Cf. A216495, A094383, A216498, A216468.

Sequence in context: A034847 A139925 A243439 * A139877 A290706 A044081

Adjacent sequences: A216494 A216495 A216496 * A216498 A216499 A216500

Keyword

nonn

Author

Alex Ratushnyak, Sep 08 2012

Status

approved