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Search: id:A161896
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| A161896 |
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Integers n for which k = (9^n - 3 * 3^n - 4n) / (2n * (2n + 1)) is an integer |
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+0
5
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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).
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CROSSREFS
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Cf. A161897 A000040, A002515, A005384 A158034, A158035, A158036 A145918
Adjacent sequences: A161893 A161894 A161895 this_sequence A161897 A161898 A161899
Sequence in context: A069097 A024921 A152533 this_sequence A143127 A061769 A143125
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KEYWORD
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easy,nonn
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AUTHOR
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Reikku Kulon (reikku(AT)gmail.com), Jun 21 2009
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