|
Search: id:A119480
|
|
|
| A119480 |
|
Numbers n such that the Bernoulli number B_{4n} has denominator 30. |
|
+0
1
|
|
| 1, 2, 17, 19, 31, 38, 47, 59, 61, 62, 71, 94, 101, 103, 107, 109, 118, 122, 137, 149, 151, 157, 167, 181, 197, 206, 211, 218, 223, 227, 229, 241, 257, 263, 269, 271, 283, 289, 302, 311, 313, 314, 317, 331, 334, 337, 347, 349, 353, 361, 362, 367, 379
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Most a(n) are primes from A043297(n) except for a(1) = 1 and composite a(n) for n=6,10,12,17,18,26,28,38,39,42,45,50,51, ... a(6) = 38 = 2*19, a(10) = 62 = 2*31, a(12) = 94 = 2*47, a(17) = 118 = 2*59, a(18) = 122 = 2*61, a(26) = 206 = 2*103, a(28) = 218 = 2*109, a(38) = 289 = 17*17, a(39) = 302 = 2*151, a(42) = 314 = 2*157, a(45) = 334 = 2*167, a(50) = 361 = 19*19, a(51) = 362 = 2*181, ... It appears that most composite a(n) are the doubles of some primes from A043297(n) belonging to A081092[n] and A045404[n] - Primes congruent to {3, 4, 5, 6} mod 7. The rest of composite a(n) are the squares of the primes from A043297(n).
Some a(n) are the products of different primes from A043297(n), for example a(77) = 527 = 17*31. a(n) belong to A045402 Primes congruent to {1, 3, 4, 5, 6} mod 7. a(n) is a subset of A053176 Primes p such that 2p+1 is composite, A045979 Bernoulli number B_{2n} has denominator 6, A090863 Numbers n such that F(n+1)*F(n-1)*B(2n) is an integer, where F(k)=k-th Fibonacci number and B(2k)=2k-th Bernoulli number. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 27 2006
|
|
FORMULA
|
a(n) = A051225[n]/2.
|
|
CROSSREFS
|
Cf. A043297, A051225, A051222, A051230, A045404.
Cf. A045402, A053176, A045979, A090863.
Sequence in context: A074857 A133247 A080115 this_sequence A043297 A018569 A022118
Adjacent sequences: A119477 A119478 A119479 this_sequence A119481 A119482 A119483
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 26 2006
|
|
|
Search completed in 0.002 seconds
|
