login
A031932
Lower prime of a pair of consecutive primes having a difference of 14.
14
113, 293, 317, 773, 839, 863, 953, 1409, 1583, 1847, 2039, 2357, 2423, 2633, 2753, 2819, 2939, 3023, 3593, 3677, 3779, 3833, 3863, 4139, 4493, 4817, 4889, 4973, 5153, 5309, 5333, 5669, 5939, 6053, 6719, 7043, 7193, 7283, 7607, 7703
OFFSET
1,1
COMMENTS
Conjecture: The sequence is infinite and for every n, a(n+1) < a(n)^(1+1/n); i.e., 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
FORMULA
a(n) = prime(A320705(n)). - R. J. Mathar, Apr 30 2024
MATHEMATICA
Transpose[Select[Partition[Prime[Range[1000]], 2, 1], Last[#]-First[#] == 14&]] [[1]] (* Harvey P. Dale, Aug 24 2012 *)
PROG
(Magma) [p: p in PrimesUpTo(8000) | NextPrime(p)-p eq 14]; // Bruno Berselli, Apr 09 2013
(PARI) is(n)=isprime(n) && nextprime(n+1)==n+14 \\ Charles R Greathouse IV, Sep 14 2015
CROSSREFS
Subsequence of A124586.
Cf. A248855.
Sequence in context: A059331 A124586 A051110 * A216310 A211445 A172983
KEYWORD
nonn
AUTHOR
STATUS
approved