A216498 Primes p with property that there exists a number d>0 such that numbers p-k*d, k=1...5, are five primes.

157, 257, 311, 353, 463, 509, 691, 757, 823, 839, 881, 907, 941, 953, 1063, 1097, 1223, 1229, 1249, 1297, 1301, 1307, 1439, 1459, 1531, 1583, 1669, 1723, 1777, 1879, 1907, 1913, 1931, 2027, 2087, 2089, 2141, 2143, 2179, 2207, 2293, 2351, 2371, 2377, 2399, 2411

Offset

1,1

Comments

Conjecture: only 9198 primes are not in the sequence: 2, 3, ..., 2521081.

Links

Table of n, a(n) for n=1..46.

Example

157 is in the sequence because with d=30: 127, 97, 67, 37, 7 are all primes.

Mathematica

prms = 5; 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[2411]]], fQ] (* T. D. Noe, Sep 08 2012 *)

Prog

(PARI) is(n)=my(t); forprime(p=2, n-16, if((n-p)%5==0 && isprime((t=(n-p)/5)+p) && isprime(2*t+p) && isprime(3*t+p) && isprime(4*t+p) && isprime(n), return(1))); 0 \\ Charles R Greathouse IV, Sep 10 2014

Crossrefs

Cf. A216495, A094383, A216497, A216468.

Sequence in context: A142231 A020356 A142367 * A275317 A303094 A001837

Adjacent sequences: A216495 A216496 A216497 * A216499 A216500 A216501

Keyword

nonn

Author

Alex Ratushnyak, Sep 08 2012

Status

approved