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A301806 Numbers k such that the concatenation of 2^k - 1 and 2^(k - 1) - 1 is prime.

%I A301806 #403 Feb 25 2024 06:02:41
%S A301806 2,3,4,7,8,12,19,22,36,46,51,67,79,215,359,394,451,1323,2131,3336,
%T A301806 3371,6231,19179,39699,51456,56238,69660,75894,79798,92020,174968,
%U A301806 176006,181015,285019,331259,360787,366770
%N A301806 Numbers k such that the concatenation of 2^k - 1 and 2^(k - 1) - 1 is prime.
%C A301806 541456 is a term. - _Paolo Galliani_, Feb 12 2020
%e A301806 2 is in the sequence because the concatenation of 3 and 1 is 31, which is prime.
%e A301806 3 is in the sequence because the concatenation of 7 and 3 is 73, which is prime.
%e A301806 5 is not in the sequence because the concatenation of 31 and 15 is 3115 = 5 * 7 * 89.
%t A301806 Select[Range[10^3], PrimeQ@ FromDigits[Join @@ IntegerDigits@ {2^# - 1, 2^(# - 1) - 1}] &] (* _Michael De Vlieger_, Oct 17 2018 *)
%o A301806 (PFGW) ABC2 (2^$a-1)*10^len(2^($a-1)-1)+2^($a-1)-1 a: from x to y
%o A301806 (PARI) isok(n) = isprime(eval(concat(Str(2^n-1), Str(2^(n-1)-1)))); \\ _Michel Marcus_, Mar 27 2018
%Y A301806 Cf. A000040, A000225, A298613 (associated primes).
%K A301806 nonn,base,more
%O A301806 1,1
%A A301806 _Paolo Galliani_, Mar 27 2018
%E A301806 a(33) from _Paolo Galliani_, May 02 2018
%E A301806 a(34) from _Paolo Galliani_, Jun 14 2018
%E A301806 a(35) from _Paolo Galliani_, Jul 17 2018
%E A301806 a(36)-a(37) from _Paolo Galliani_, Aug 27 2018