A273009 Numbers k such that (2^k + 5) / 3 is prime.

0, 2, 4, 6, 12, 18, 24, 42, 84, 300, 390, 780, 822, 2430, 5508, 5514, 6492, 12372, 22680, 25770, 169416, 174240, 383544, 1007838, 1572882

Offset: 1

Author

Vincenzo Librandi, May 13 2016

Keywords

• nonn
• more
• hard

Comments

Larger members of the sequence generate probable primes only.

Corresponding prime numbers are: 2, 3, 7, 23, 1367, 87383, 5592407, 1466015503703,6447604371278022265099607,.. etc.

Links

• Henri & Renaud Lifchitz, (2^n+5)/3 PRPs [PRP Top Records]

Crossrefs

Cf. A261539.

Programs

Magma

[n: n in [0..2000] | (2^n+5) mod 3 eq 0 and IsPrime((2^n+5) div 3)];

Mathematica

Select[Range[0,10000], PrimeQ[(2^# + 5)/3] &]

PARI

is(n)=ispseudoprime((2^n+5)/3) \\ Charles R Greathouse IV, Jun 07 2016

Formula

a(n) = 2*A261539(n).