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A031930
Lower prime of a difference of 12 between consecutive primes.
15
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
FORMULA
a(n) = prime(A320704(n)). - R. J. Mathar, Apr 30 2024
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
KEYWORD
nonn
AUTHOR
STATUS
approved