A358198 a(n) is the first member p of A007530 such that, with q = p+2, r = p+6 and s = p+8, (2*p+q)/5 is a prime and (r+2*s)/5^n is a prime.

11, 101, 243701, 6758951, 3257480201, 5493848951, 58634348951, 218007942701, 21840280598951, 213065296223951, 186522444661451, 383378987630201, 7794174397786451, 110420241292317701, 67327687581380201, 91455128987630201, 3987035878499348951, 80659241994222005201, 4289429982503255201

Offset: 1

Author

J. M. Bergot and Robert Israel, Nov 02 2022

Keywords

• nonn

Examples

			a(3) = 243701 because p = 247301, q = p+2 = 247303, r = p+6 = 243707, s = p+8 = 243709, (2*p+q)/5 = 146221 and (r+2*s)/5^3 = 5849 are primes, and p is the least prime that works.
		

Crossrefs

Cf. A007530, A358149.

Programs

Maple

f:= proc(n) local t,p,m;
        m:= 5^n;
        t:= 3;
        do
          t:= nextprime(t);
          if t*m mod 3 <> 1 then next fi;
          p:= (t*m-22)/3;
          if isprime(p) and isprime(p+2) and isprime(p+6) and isprime(p+8) and isprime((3*p+2)/5) then return p fi;
        od;
end proc;
map(f, [$1..20]);

Mathematica

a[n_] := a[n] = Module[{t = 3, p, m = 5^n}, While[True, t = NextPrime[t]; If[Mod[t*m, 3] != 1, Continue[]]; p = (t*m - 22)/3; If[AllTrue[{p, p+2, p+6, p+8, (3p+2)/5}, PrimeQ], Return[p]]]];
Table[Print[n, " ", a[n]]; a[n], {n, 1, 19}] (* Jean-François Alcover, Jan 31 2023, after Maple program *)