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A161896 Integers n for which k = (9^n - 3 * 3^n - 4n) / (2n * (2n + 1)) is an integer. 5
5, 11, 23, 29, 41, 53, 83, 89, 113, 131, 173, 179, 191, 233, 239, 251, 281, 293, 359, 419, 431, 443, 491, 509, 593, 641, 653, 659, 683, 719, 743, 761, 809, 911, 953, 1013, 1019, 1031, 1049, 1103, 1223, 1229, 1289, 1409, 1439, 1451, 1481, 1499, 1511, 1541, 1559 (list; graph; refs; listen; history; text; internal format)
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

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).

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

Cf. A161897 A000040, A002515, A005384, A158034, A158035, A158036, A145918, A002943.

Sequence in context: A192761 A152533 A228485 * A317909 A304372 A167610

Adjacent sequences:  A161893 A161894 A161895 * A161897 A161898 A161899

KEYWORD

easy,nonn

AUTHOR

Reikku Kulon, Jun 21 2009

STATUS

approved

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Last modified November 19 03:40 EST 2019. Contains 329310 sequences. (Running on oeis4.)