A216468 Primes p with property that there exists a number d>0 such that numbers p-k*d, k=1...6, are six primes.

907, 1307, 1439, 1459, 1669, 1879, 2089, 2141, 2351, 2713, 4139, 4759, 4969, 5179, 5417, 6047, 6101, 6353, 6779, 6793, 7919, 8369, 8663, 9049, 9349, 9491, 9533, 9623, 9769, 10099, 10691, 10883, 11083, 11213, 11369, 11399, 11621, 11789, 11887, 11923, 12097, 12119

Offset

1,1

Comments

Conjecture: only 312722 primes are not in the sequence: 2, 3, ..., 198702899.

Links

Table of n, a(n) for n=1..42.

Example

907 is in the sequence because with d = 150: 7, 157, 307, 457, 607, 757 are all primes.

Mathematica

fQ[p_] := Module[{d = 1}, While[6*d < p && Union[PrimeQ[p - Range[6]*d]] != {True}, d++]; 6*d < p]; Select[Prime[Range[4, PrimePi[12119]]], fQ] (* T. D. Noe, Sep 07 2012 *)

Prog

(PARI) is(n)=my(t); forprime(p=2, n-20, if((n-p)%6==0 && isprime((t=(n-p)/6)+p) && isprime(2*t+p) && isprime(3*t+p) && isprime(4*t+p) && isprime(5*t+p) && isprime(n), return(1))); 0 \\ Charles R Greathouse IV, Sep 10 2014

Crossrefs

Cf. A215895, A216495, A094383, A216497, A216498.

Sequence in context: A174862 A350852 A195987 * A031939 A253228 A134075

Adjacent sequences: A216465 A216466 A216467 * A216469 A216470 A216471

Keyword

nonn

Author

Alex Ratushnyak, Sep 07 2012

Status

approved