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.

211050, 248640, 253680, 410340, 507360, 605640, 1121190, 1138830, 1262100, 2162580, 2172870, 2277660, 4070220, 6305460, 7671510, 11659410, 12577110, 14203770, 14862120, 17472840, 18728640, 18798360, 20520570, 21140700

Offset: 1

Author

Don Reble, Apr 09 2002

Keywords

• nonn

Examples

			211050 is in the sequence because 211049, 211051, 422099, 422101, 844199 and 844201 are all prime.
		

Crossrefs

Cf. A066388.

Programs

Maple

isA069175 := proc(k)
    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
        true ;
    else
        false;
    end if;
end proc:
n := 1 :
for k from 4 by 2 do # create b-file
    if isA069175(k) then
        printf("%d %d\n",n,k) ;
        n := n+1 ;
    end if;
end do: # R. J. Mathar, Nov 02 2023

Mathematica

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 *)
Select[Range[21150000],AllTrue[{#-1,#+1,2#-1,2#+1,4#-1,4#+1},PrimeQ]&] (* Harvey P. Dale, Aug 19 2025 *)

Extensions

Offset changed to 1 by Georg Fischer, Sep 23 2022