A187733 Primes of the form 2^n + n + 2.

3, 5, 13, 137, 523, 524309, 134217757, 8589934627, 178405961588244985132285746181186892047843477

Offset: 1

Author

Jaroslav Krizek, Jan 19 2013

Keywords

• nonn

Comments

The list of associated n is: 0, 1, 3, 7, 9, 19, 27, 33, 147, 639, ...

Primes from A052968 of the form 2^(n-1) + n + 1 for n = 1, 2, 4, 8, 10, 20, 28, 34, ...

Pairs of twin primes of forms (2^n+n; 2^n+n+2): (3; 5), (11; 13), (521; 523), ...

The prime number a(10) = 2^639 + 639 + 2 has 193 digits.

a(11) = 2^12243 + 12243 + 2 and a(12) = 2^41427 + 41427 + 2. - Giovanni Resta, Jan 23 2013

The sequence contains the subsequence 13, 137, 524309,... where the n themselves are prime, n = 3, 7, 19 (no further up to 41427). - Jaroslav Krizek, Feb 27 2013

Examples

			8589934627 is in the sequence since 8589934627 =  2^33 + 33 + 2 and 8589934627 is prime.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10
• FactorDB, 2^n + n + 2.

Crossrefs

Cf. A052968, A129962, A309328.

Programs

Mathematica

Select[Table[2^n + n + 2, {n, 60}], PrimeQ[#] &]