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A069175 Numbers k such that k-1, k+1, 2*k-1, 2*k+1, 4*k-1 and 4*k+1 are all prime.

%I A069175 #17 Aug 19 2025 18:08:43
%S A069175 211050,248640,253680,410340,507360,605640,1121190,1138830,1262100,
%T A069175 2162580,2172870,2277660,4070220,6305460,7671510,11659410,12577110,
%U A069175 14203770,14862120,17472840,18728640,18798360,20520570,21140700
%N A069175 Numbers k such that k-1, k+1, 2*k-1, 2*k+1, 4*k-1 and 4*k+1 are all prime.
%e A069175 211050 is in the sequence because 211049, 211051, 422099, 422101, 844199 and 844201 are all prime.
%p A069175 isA069175 := proc(k)
%p A069175     if isprime(k-1) and isprime(k+1) and isprime(2*k-1) and isprime(2*k+1) and isprime(4*k-1) and isprime(4*k+1) then
%p A069175         true ;
%p A069175     else
%p A069175         false;
%p A069175     end if;
%p A069175 end proc:
%p A069175 n := 1 :
%p A069175 for k from 4 by 2 do # create b-file
%p A069175     if isA069175(k) then
%p A069175         printf("%d %d\n",n,k) ;
%p A069175         n := n+1 ;
%p A069175     end if;
%p A069175 end do: # _R. J. Mathar_, Nov 02 2023
%t A069175 lst={};Do[If[PrimeQ[n-1]&&PrimeQ[n+1]&&PrimeQ[2*n-1]&&PrimeQ[2*n+1]&&PrimeQ[4*n-1]&&PrimeQ[4*n+1],Print[n];AppendTo[lst,n]],{n,11!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 05 2009 *)
%t A069175 Select[Range[21150000],AllTrue[{#-1,#+1,2#-1,2#+1,4#-1,4#+1},PrimeQ]&] (* _Harvey P. Dale_, Aug 19 2025 *)
%Y A069175 Cf. A066388.
%K A069175 nonn
%O A069175 1,1
%A A069175 _Don Reble_, Apr 09 2002
%E A069175 Offset changed to 1 by _Georg Fischer_, Sep 23 2022