A074259 Gaps between primes p such that 2p+1 is also prime, i.e., Sophie-Germain primes A005384.

1, 2, 6, 12, 6, 12, 12, 30, 6, 24, 18, 42, 6, 12, 42, 6, 12, 30, 12, 66, 60, 12, 12, 48, 18, 84, 48, 12, 6, 24, 36, 24, 18, 48, 102, 42, 60, 6, 12, 18, 54, 120, 6, 60, 120, 30, 12, 30, 18, 12, 48

Offset

1,2

Comments

The first two consecutive identical gaps are 12, 12 between A005384(6..8) = (29, 41, 53).

The first three, four and five identical gaps in a row are equal to 30, 150 and 420, respectively, and occur after A005384(85) = 3299, A005384(29952) = 4866623, and A005384(32361449747) = 22081407211439. These were found by N. Fernandez and G. Resta, see link to discussion on the SeqFan mailing list. - M. F. Hasler, Sep 18 2016

Links

M. F. Hasler, Table of n, a(n) for n = 1..7745

Giovanni Resta, in reply to Harvey P. Dale and others, Re: Consecutive Sophie Germain primes with the same gap, SeqFan mailing list, Sep. 2016. (Click "Previous message" to see Neil Fernandez' earlier results.)

Mathematica

Select[Prime[Range[500]], PrimeQ[2#+1]&]//Differences (* Harvey P. Dale, Jul 15 2019 *)

Prog

(PARI) c=0; forprime(p=1+L=2, 10^6, if(isprime(2*p+1), write("primegap.txt", c++, " "p-L); L=p)) \\ Edited by M. F. Hasler, Sep 16 2016

Crossrefs

First differences of A005384.

Sequence in context: A205103 A165822 A014965 * A338376 A113540 A111658

Adjacent sequences: A074256 A074257 A074258 * A074260 A074261 A074262

Keyword

nonn

Author

Jon Perry, Sep 20 2002

Extensions

Edited (name, offset, more terms) by M. F. Hasler, Sep 16 2016

Status

approved