A031930 Lower prime of a difference of 12 between consecutive primes.

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

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

Aside from 2 and 3, all primes are congruent to 1, 5, 7, 11 mod 12. Thus the least significant duodecimal digit of any term in this sequence is 1, 5, 7 or B. - Alonso del Arte, Aug 19 2017

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 199 + 12 = 211.
211 is also a term since the next prime is 211 + 12 = 223.
But 223 is not a term since the next prime is 227, and 223 + 12 = 235 = 5 * 47.

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, A031928.

Sequence in context: A128312 A106628 A109561 * A160342 A225575 A252667

Adjacent sequences: A031927 A031928 A031929 * A031931 A031932 A031933

Keyword

nonn

Author

Jeff Burch

Status

approved