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A074259 Gaps between primes p such that 2p+1 is also prime, i.e., Sophie-Germain primes A005384. 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A113540 A111658 A105692

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

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Last modified December 8 04:31 EST 2019. Contains 329850 sequences. (Running on oeis4.)