A141592 Numbers k such that k, k + 210*1, k + 210*2, k + 210*3, k + 210*4 are averages of pairs of twin primes.

1308498, 3042492, 3042702, 7445310, 20031102, 31572522, 44687988, 54266292, 141208620, 182316522, 237416370, 357080022, 448436322, 611641188, 699458412, 761126028, 774997368, 794065968, 836452962, 915215592, 944958942, 1009194618, 1581935940, 1763255562, 1871007372

Offset

1,1

Links

Table of n, a(n) for n=1..25.

Example

1308498 and 1308708, 1308918, 1309128, 1309338 are averages of twin primes.
3042492 and 3042702, 3042912, 3043122, 3043332 are averages of twin primes.

Mathematica

q=210; lst={}; Do[If[PrimeQ[n-1]&&PrimeQ[n+1]&&PrimeQ[n+q*1-1]&& PrimeQ[n+q*1+1]&& PrimeQ[n+q*2-1]&&PrimeQ[n+q*2+1]&& PrimeQ[n+q*3-1]&& PrimeQ[n+q*3+1]&& PrimeQ[n+q*4-1]&&PrimeQ[n+q*4+1], AppendTo[lst, n]], {n, 10^8}]; lst
Select[Range[55*10^6], AllTrue[{#-1, #+1, #+209, #+211, #+419, #+421, #+629, #+631, #+839, #+841}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 08 2017 *)

Prog

(Magma) [k:k in [1..55000000]|forall{m:m in [0, 210, 420, 630, 840]|IsPrime(k+m-1) and IsPrime(k+m+1)}]; // Marius A. Burtea, Jan 13 2020

Crossrefs

Cf. A001097, A001359, A006512, A014574.

Sequence in context: A186138 A066702 A261731 * A234710 A116495 A179584

Adjacent sequences: A141589 A141590 A141591 * A141593 A141594 A141595

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Aug 20 2008

Extensions

Edited by N. J. A. Sloane, Aug 24 2008

a(9)-a(25) from Amiram Eldar, Jan 13 2020

Status

approved