A141594 Numbers k such that k, q+k, 2*q+k, 3*q+k, 4*q+k, and 5*q+k are all averages of twin primes, where q is the product of the first 8 primes.

6341442, 6837222, 11285508, 15315720, 174710022, 326603400, 434021520, 508246812, 711829818, 1177207878, 1442665452, 1802819172, 1917309882, 2010186978, 2055080892, 2502111192, 2692872672, 2926907538, 3101732970, 3111432660, 3167425578, 3487611162, 3497310852, 3592253772

Offset

1,1

Comments

q = 2*3*5*7*11*13*17*19 = 9699690.

Links

David A. Corneth, Table of n, a(n) for n = 1..164 (Terms <= 10^11)

Example

6341442, q+6341442, 2*q+6341442, 3*q+6341442, 4*q+6341442, and 5*q+6341442 are all averages of twin primes, so 6341442 is a term.

Mathematica

q=9699690; 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] && PrimeQ[n+q*5-1] && PrimeQ[n+q*5+1], Print[n]; AppendTo[lst, n]], {n, 10^6, 10^9}];
lst
mkQ[k_]:=Module[{q=Times@@Prime[Range[8]]}, AllTrue[Flatten[Table[x q+k+{1, -1}, {x, 0, 5}], 1], PrimeQ]]; Select[Range[154*10^5], mkQ] (* The program generates the first 4 terms of the sequence. To generate more, increase the Range constant but the program may take a long time to run. *) (* Harvey P. Dale, Apr 09 2023 *)

Prog

(PARI) is(n) = { for(i = 0, 5, if(!isprime(n + i*9699690 - 1), return(0) ); if(!isprime(n + i*9699690 + 1), return(0) ); ); 1 } \\ David A. Corneth, Feb 24 2021

Crossrefs

Sequence in context: A147531 A018895 A178135 * A307019 A234758 A295481

Adjacent sequences: A141591 A141592 A141593 * A141595 A141596 A141597

Keyword

nonn,less

Author

Vladimir Joseph Stephan Orlovsky, Aug 20 2008

Extensions

Edited by Jon E. Schoenfield, Feb 24 2021

Status

approved