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A031928
Lower prime of a difference of 10 between consecutive primes.
24
139, 181, 241, 283, 337, 409, 421, 547, 577, 631, 691, 709, 787, 811, 829, 919, 1021, 1039, 1051, 1153, 1171, 1249, 1399, 1471, 1627, 1699, 1723, 1801, 1879, 2017, 2029, 2053, 2089, 2143, 2521, 2647, 2719, 2731, 2767, 2887, 2917, 3001, 3109, 3361, 3517, 3547, 3571, 3583, 3709, 3769, 3823, 3853, 4201, 4219, 4231, 4243, 4261, 4273, 4327, 4339, 4363, 4483, 4663, 4861, 4909, 4957, 5011, 5179, 5323, 5581, 5659, 5701, 5791, 5869, 6079, 6091
OFFSET
1,1
COMMENTS
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 comments at A248855). - Jahangeer Kholdi and Farideh Firoozbakht, Nov 29 2014
FORMULA
a(n) = prime(A320703(n)). - R. J. Mathar, Apr 30 2024
MATHEMATICA
Transpose[Select[Partition[Prime[Range[800]], 2, 1], #[[2]] - #[[1]] == 10&]] [[1]] (* Harvey P. Dale, Oct 02 2014 *)
p = Prime@Range@800; p[[Flatten@Position[Differences@p, 10]]] (* Hans Rudolf Widmer, Aug 28 2022 *)
PROG
(Magma) [p: p in PrimesUpTo(7000) | NextPrime(p)-p eq 10]; // Bruno Berselli, Apr 09 2013
(PARI) forprime(p=o=1, 1e4, 10+o==(o=p)&&print1(p-10", ")) \\ M. F. Hasler, Mar 10 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Lekraj Beedassy, Jul 23 2003
EXTENSIONS
Edited by Labos Elemer, Jul 25 2003
STATUS
approved