OFFSET
1,1
COMMENTS
Near superset of the Sophie Germain primes (A005384), excluding 2 and 3: 2n + 1 is prime. Nearly all members of this sequence are also prime, but four members less than 10000 are composite: 1541 = 23 * 67, 2465 = 5 * 17 * 29, 3281 = 17 * 193, and 4961 = 11^2 * 41.
The congruence of n modulo 4 is evenly distributed between 1 and 3. n is congruent to 5 (mod 6) for all n less than two billion.
This sequence has roughly twice the density of the sequence (A158034) corresponding to the Diophantine equation
f = (4^n - 2^n + 8n^2 - 2) / (2n * (2n + 1)),
and contains most members of that sequence. Those it does not contain are composite and often congruent to 3 (mod 6).
Composite terms appear to predominantly belong to A262051. - Bill McEachen, Aug 29 2024
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
PROG
(Haskell)
a161896 n = a161896_list !! (n-1)
a161896_list = [x | x <- [1..],
(9^x - 3*3^x - 4*x) `mod` (2*x*(2*x + 1)) == 0]
-- Reinhard Zumkeller, Jan 12 2014
(PARI) is(n)=my(m=2*n*(2*n+1), t=Mod(3, m)^n); t^2-3*t==4*n \\ Charles R Greathouse IV, Nov 25 2014
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Reikku Kulon, Jun 21 2009
STATUS
approved