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%I #6 Nov 27 2022 11:06:32
%S 2,2,160,140,2800,8660,62150,4085530,922820,4629490,5802710,
%T 1146175000,90894850
%N Smallest b > 1 such that b^(2^n)+1 is a Sophie Germain prime.
%C In other words, 2*b^(2^n)+3 is also prime.
%C For n > 1, a(n) ends in 0 because b is even (or else b^(2^n)+1 would have 2 as a proper divisor) and b == 0 (mod 5) (or else 2*b^(2^n)+3 would have 5 as a proper divisor).
%H PrimeGrid and "Stream", <a href="https://www.primegrid.com/forum_thread.php?id=9538">GFN-1x Small Primes search</a>, mentions a(12).
%o (PARI) a(n)=n<2&&return(2);forstep(b=10,+oo,10,ispseudoprime(b^(2^n)+1)&&ispseudoprime(2*b^(2^n)+3)&&return(b))
%Y Cf. A005384, A056993, A182154.
%K nonn,hard,more
%O 0,1
%A _Jeppe Stig Nielsen_, Nov 23 2022