

A119480


Numbers n such that the Bernoulli number B_{4n} has denominator 30.


29



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
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OFFSET

1,2


COMMENTS

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(n1)*B(2n) is an integer, where F(k)=kth Fibonacci number and B(2k)=2kth Bernoulli number.  Alexander Adamchuk, Jul 27 2006


LINKS

E. PĂ©rez Herrero, Table of n, a(n) for n=1..50000


FORMULA

a(n) = A051225[n]/2.


MATHEMATICA

Select[Range@ 400, Denominator@ BernoulliB[4 #] == 30 &] (* Michael De Vlieger, Aug 09 2017 *)


CROSSREFS

Cf. A043297, A051225, A051222, A051230, A045404.
Cf. A045402, A053176, A045979, A090863.
Sequence in context: A176902 A153261 A080115 * A043297 A018569 A022118
Adjacent sequences: A119477 A119478 A119479 * A119481 A119482 A119483


KEYWORD

nonn


AUTHOR

Alexander Adamchuk, Jul 26 2006


STATUS

approved



