

A124588


Primes p such that qp <= 2, where q is the next prime after p.


7



2, 3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 461, 521, 569, 599, 617, 641, 659, 809, 821, 827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319, 1427, 1451, 1481, 1487, 1607
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OFFSET

1,1


COMMENTS

Consists of 2 together with the lower members of twin primes, A001359. See the latter entry for references.
"Assuming certain (admittedly difficult) conjectures on the distribution of primes in arithmetic progressions, [GoldstonPintzYildirim] prove the existence of infinitely many prime pairs that differ at most by 16."  Soundararajan
Lesser of twin primes together with 2; union with A029710 gives A124589.  Reinhard Zumkeller, Dec 23 2006
Primes p such that either p+3/2+1/2 is prime. [JuriStepan Gerasimov, Jan 29 2010]
The prime differences of 2 primes (without repetition). [JuriStepan Gerasimov, Jun 01 2010, Jun 08 2010]


LINKS

Table of n, a(n) for n=1..52.
K. Soundararajan, Small gaps between prime numbers: the work of GoldstonPintzYildirim, Bull. Amer. Math. Soc., 44 (2007), 118.
Index entries for primes, gaps between


MATHEMATICA

Transpose[Select[Partition[Prime[Range[300]], 2, 1], #[[2]]#[[1]]<3&]] [[1]] (* Harvey P. Dale, Feb 11 2015 *)


PROG

(PARI) print1(2", "); (for(x=1, 200, print1(twinl(x)", "))) \\ Cino Hilliard, Mar 29 2008


CROSSREFS

Cf. A001359.
Sequence in context: A038909 A073534 A063091 * A059428 A084571 A345471
Adjacent sequences: A124585 A124586 A124587 * A124589 A124590 A124591


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Dec 19 2006; edited May 15 2008 at the suggestion of R. J. Mathar


STATUS

approved



