|
%I #18 Apr 09 2023 09:33:06
%S 6341442,6837222,11285508,15315720,174710022,326603400,434021520,
%T 508246812,711829818,1177207878,1442665452,1802819172,1917309882,
%U 2010186978,2055080892,2502111192,2692872672,2926907538,3101732970,3111432660,3167425578,3487611162,3497310852,3592253772
%N 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.
%C q = 2*3*5*7*11*13*17*19 = 9699690.
%H David A. Corneth, <a href="/A141594/b141594.txt">Table of n, a(n) for n = 1..164</a> (Terms <= 10^11)
%e 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.
%t q=9699690; lst={};
%t 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}];
%t lst
%t 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 *)
%o (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
%K nonn,less
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Aug 20 2008
%E Edited by _Jon E. Schoenfield_, Feb 24 2021
|
