|
| |
|
|
A161896
|
|
Integers n for which k = (9^n - 3 * 3^n - 4n) / (2n * (2n + 1)) is an integer
|
|
4
|
|
|
|
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
|
Table of n, a(n) for n=1..51.
|
|
|
CROSSREFS
|
Cf. A161897 A000040, A002515, A005384 A158034, A158035, A158036 A145918
Sequence in context: A189978 A192761 A152533 * A167610 A143127 A061769
Adjacent sequences: A161893 A161894 A161895 * A161897 A161898 A161899
|
|
|
KEYWORD
|
easy,nonn
|
|
|
AUTHOR
|
Reikku Kulon, Jun 21 2009
|
|
|
STATUS
|
approved
|
| |
|
|
