A216590 Primes p with property that there exists a number d>0 such that numbers p-k*d, k=1...7, are seven primes.

1669, 1879, 2089, 2351, 4969, 5179, 6047, 10883, 11923, 12097, 12143, 12329, 12539, 12763, 13049, 13183, 15413, 15923, 16187, 16547, 16741, 17189, 17581, 18481, 19993, 20201, 21433, 21727, 22303, 22483, 23021, 23053, 23831, 24023, 24749, 25579, 25633, 26111, 26561

Offset

1,1

Comments

Conjecture: only 5254157 primes are not in the sequence: 2, 3, ..., 5082095279.

Conjecture: for any k>0 there exists p0 such that for any prime p>p0 there exists a k-term arithmetic progression of primes with p at the end.

Links

Table of n, a(n) for n=1..39.

Example

1669 is in the sequence because with d=210: 1459, 1249, 1039, 829, 619, 409, 199 are all primes.

Prog

(PARI) is(n)=my(t); forprime(p=2, n-26, if((n-p)%7==0 && isprime((t=(n-p)/7)+p) && isprime(2*t+p) && isprime(3*t+p) && isprime(4*t+p) && isprime(5*t+p) && isprime(6*t+p) && isprime(n), return(1))); 0 \\ Charles R Greathouse IV, Sep 10 2014

Crossrefs

Cf. A216495, A094383, A216497, A216498, A216468.

Sequence in context: A321001 A054812 A020392 * A098974 A109564 A188008

Adjacent sequences: A216587 A216588 A216589 * A216591 A216592 A216593

Keyword

nonn

Author

Alex Ratushnyak, Sep 09 2012

Status

approved