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

1,1

Comments

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

Links

Table of n, a(n) for n=1..37.

Example

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.

Mathematica

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

Prog

(PFGW) ABC2 (2^$a-1)*10^len(2^($a-1)-1)+2^($a-1)-1 a: from x to y
(PARI) isok(n) = isprime(eval(concat(Str(2^n-1), Str(2^(n-1)-1)))); \\ Michel Marcus, Mar 27 2018

Crossrefs

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

Sequence in context: A051213 A340111 A211659 * A066847 A370121 A057887

Adjacent sequences: A301803 A301804 A301805 * A301807 A301808 A301809

Keyword

nonn,base,more

Author

Paolo Galliani, Mar 27 2018

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

Status

approved