

A174165


Numbers n for which (prime(n)  1)^2 +1 is prime.


0



1, 2, 3, 4, 5, 7, 12, 13, 19, 31, 32, 36, 37, 42, 47, 53, 54, 55, 58, 60, 63, 78, 79, 82, 83, 91, 94, 102, 105, 106, 118, 125, 126, 133, 135, 144, 155, 156, 159, 161, 163, 178, 184, 190, 206, 210, 214, 216, 219, 247, 248, 284, 286, 288, 307, 313, 315, 322
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


LINKS

Table of n, a(n) for n=1..58.


EXAMPLE

a(1) = 1 because (1st prime 1)^2 +1 = (21)^2 +1 = 2, a prime; a(2) = 2 because (2nd prime 1)^2 +1 = (31)^2 +1 = 5, a prime; a(3) = 3 because (3rd prime 1)^2 +1 = (51)^2 +1 = 17, a prime; ... ; a(6) # 6 since (6th prime 1)^2 = (131)^2 +1 = 145 = 5*29, which is not a prime; etc.


MATHEMATICA

fQ[n_] := PrimeQ[ (Prime@n  1)^2 + 1]; Select[ Range@ 335, fQ@# &]


CROSSREFS

Cf. A000040, A006093, A005722 & A127435.
Sequence in context: A143284 A279065 A015856 * A240732 A060437 A133428
Adjacent sequences: A174162 A174163 A174164 * A174166 A174167 A174168


KEYWORD

nonn


AUTHOR

JuriStepan Gerasimov, Mar 10 2010


EXTENSIONS

Edited, corrected and extended by Robert G. Wilson v, Mar 14 2010


STATUS

approved



