A074325 Difference between (1+2^n)-th and (2^n)-th primes. Also number of terms in blocks of A073798.

1, 2, 4, 4, 6, 6, 2, 8, 2, 2, 6, 18, 18, 30, 8, 24, 6, 2, 18, 4, 26, 30, 34, 2, 10, 30, 10, 2, 30, 6, 70, 4, 12, 22, 6, 24, 26, 10, 88, 2, 50, 18, 6, 20, 14, 4, 12, 6, 2, 56, 4, 30, 42, 6, 70, 74, 14, 60, 170, 14, 44, 22, 52, 36, 96, 6, 86, 86, 72, 48, 42, 18, 20, 24, 10, 154, 54, 20, 12

Offset: 0

Author

Labos Elemer, Aug 21 2002

Keywords

• nonn
• hard

Examples

			For n = 39: 2^39 = 549755813888, prime(549755813889) = 16149760533343, prime(549755813888) =  16149760533341, difference = 2 (just twin primes), so a(39) = 2.
		

Crossrefs

Cf. A051439, A033844, A073798, A000079, A001223.

Programs

Mathematica

Table[Prime[1+2^n] - Prime[2^n], {n, 1, 39}]

Formula

a(n) = A051439(n) - A033844(n).

a(n) = A001223(A000079(n)). - Michel Marcus, May 10 2024

Extensions

More terms from Michel ten Voorde Jun 13 2003

a(42) from Max Alekseyev, May 08 2009

Offset corrected by Max Alekseyev, Oct 24 2013

a(43)-a(57) from Chai Wah Wu, Aug 30 2019

a(58)-a(78) calculated using the data at A033844 and A051439 and added by Amiram Eldar, May 10 2024