A074325 - OEIS

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

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..78.

FORMULA

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

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

EXAMPLE

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

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A152782 A307119 A266076 * A058249 A340226 A348769

Adjacent sequences: A074322 A074323 A074324 * A074326 A074327 A074328

KEYWORD

nonn,hard

AUTHOR

Labos Elemer, Aug 21 2002

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

STATUS

approved