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A031930 Lower prime of a difference of 12 between consecutive primes. 12
199, 211, 467, 509, 619, 661, 797, 997, 1201, 1237, 1307, 1459, 1499, 1511, 1531, 1709, 1789, 1811, 1889, 2069, 2099, 2297, 2399, 2447, 2579, 2621, 2777, 2927, 3049, 3067, 3169, 3191, 3259, 3331, 3347, 3499, 3559, 3659, 3931, 3989 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Some of the terms of this sequence are primes that are separated from both their predecessor and successor primes by 12, e.g., 211, 1511, 4409, 4691, 7841, 9871, 11299, 11411, 11731.  See A053072. - Harvey P. Dale, Apr 07 2013

Conjecture: The sequence is infinite and for every n, a(n+1) < a(n)^(1+1/n). Namely a(n)^(1/n) is a strictly decreasing function of n (See comment lines of the sequence A248855). - Jahangeer Kholdi and Farideh Firoozbakht, Nov 29 2014

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Index entries for primes, gaps between

EXAMPLE

199 is a term as the next prime is 211.

MATHEMATICA

Transpose[Select[Partition[Prime[Range[600]], 2, 1], Last[#]-First[#]==12&]][[1]] (* Harvey P. Dale, Apr 07 2013 *)

PROG

(MAGMA) [p: p in PrimesUpTo(4000) | NextPrime(p)-p eq 12]; // Bruno Berselli, Apr 09 2013

(PARI) is(n)=nextprime(n+1)==n+12 && isprime(n) \\ Charles R Greathouse IV, Jul 02 2013

CROSSREFS

Cf. A053072, A248855.

Sequence in context: A128312 A106628 A109561 * A160342 A225575 A252667

Adjacent sequences:  A031927 A031928 A031929 * A031931 A031932 A031933

KEYWORD

nonn

AUTHOR

Jeff Burch

STATUS

approved

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Last modified March 29 06:34 EDT 2017. Contains 284250 sequences.