

A125713


Smallest odd prime p such that (n+1)^p  n^p is prime.


5



3, 3, 3, 3, 5, 3, 7, 7, 3, 3, 3, 17, 3, 3, 43, 5, 3, 1607, 5, 19, 127, 229, 3, 3, 3, 13, 3, 3, 149, 3, 5, 3, 23, 3, 5, 83, 3, 3, 37, 7, 3, 3, 37, 5, 3, 5, 58543, 3, 3, 7, 29, 3, 479, 5, 3, 19, 5, 3, 4663, 54517, 17, 3, 3, 5, 7, 3, 3, 17, 11, 47, 61, 19, 23, 3, 5, 19, 7, 5, 7, 3, 3
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OFFSET

1,1


COMMENTS

Corresponding smallest primes of the form (n+1)^p  n^p, where p = a(n) is an odd prime, are listed in A121091(n+1) = {7, 19, 37, 61, 4651, 127, 1273609, 2685817, 271, 331, 397, 6431804812640900941, 547, 631, ...}. a(n) = A058013(n) for n = {4, 7, 10, 12, 13, 16, 17, 19, 22, 24, 25, 27, 28, 31, ...} = A047845(n) = (n1)/2, where n runs through odd nonprimes (A014076), for n>1. a(97) = 7. a(99)a(112) = {5, 43, 5, 13, 7, 5, 3, 6529, 59, 3, 5, 5, 113, 5}. a(114) = 139. a(117)a(129) = {7, 13, 3, 5, 5, 7, 3, 5167, 3, 41, 59, 3, 3}. a(131) = 101. a(n) is currently unknown for n = {113, 115, 116, 130, 132, ...}.
a(96) = 1307, a(98) = 709.
a(137) is probably 196873 from prime of this form discovered by JeanLouis Charton in December 2009 and reported to Henri Lifchitz's PRP Top.  Robert Price, Feb 17 2012
a(138) through a(150) is 113,>32401,3,7,3,8839,5,7,13,3,5,271,13.  Robert Price, Feb 17 2012
a(137) = 196873 confirmed by Fischer link; a(139) > 260000.  Ray Chandler, Feb 26 2017


LINKS

Robert Price and Ray Chandler, Table of n, a(n) for n = 1..138 (first 136 terms from Robert Price)
Richard Fischer, Generalized primes of the form (B+1)^N  B^N.


CROSSREFS

Cf. A058013 = Smallest prime p such that (n+1)^p  n^p is prime. Cf. A065913 = Smallest prime of form (n+1)^k  n^k. Cf. A121091 = Smallest nexus prime of the form n^p  (n1)^p, where p is odd prime. Cf. A047845, A014076.
Cf. A062585 = numbers n such that k^n  (k1)^n is prime, where k is 19. Cf. A000043, A057468, A059801, A059802, A062572A062666.
Sequence in context: A176994 A264050 A262995 * A162220 A118911 A190268
Adjacent sequences: A125710 A125711 A125712 * A125714 A125715 A125716


KEYWORD

hard,nonn


AUTHOR

Alexander Adamchuk, Dec 01 2006, Feb 15 2007


STATUS

approved



