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

2, 3, 4, 7, 8, 12, 19, 22, 36, 46, 51, 67, 79, 215, 359, 394, 451, 1323, 2131, 3336, 3371, 6231, 19179, 39699, 51456, 56238, 69660, 75894, 79798, 92020, 174968, 176006, 181015, 285019, 331259, 360787, 366770

Offset: 1

Author

Paolo Galliani, Mar 27 2018

Keywords

• nonn
• base
• more

Comments

541456 is a term. - Paolo Galliani, Feb 12 2020

Examples

			2 is in the sequence because the concatenation of 3 and 1 is 31, which is prime.
3 is in the sequence because the concatenation of 7 and 3 is 73, which is prime.
5 is not in the sequence because the concatenation of 31 and 15 is 3115 = 5 * 7 * 89.
		

Crossrefs

Cf. A000040, A000225, A298613 (associated primes).

Programs

Mathematica

Select[Range[10^3], PrimeQ@ FromDigits[Join @@ IntegerDigits@ {2^# - 1, 2^(# - 1) - 1}] &] (* Michael De Vlieger, Oct 17 2018 *)

PARI

isok(n) = isprime(eval(concat(Str(2^n-1), Str(2^(n-1)-1)))); \\ Michel Marcus, Mar 27 2018

PFGW

ABC2 (2^$a-1)*10^len(2^($a-1)-1)+2^($a-1)-1 a: from x to y

Extensions

a(33) from Paolo Galliani, May 02 2018

a(34) from Paolo Galliani, Jun 14 2018

a(35) from Paolo Galliani, Jul 17 2018

a(36)-a(37) from Paolo Galliani, Aug 27 2018