

A043297


Primes p such that B(4*p) has denominator 30 where B(2n) are the Bernoulli numbers.


5



2, 17, 19, 31, 47, 59, 61, 71, 101, 103, 107, 109, 137, 149, 151, 157, 167, 181, 197, 211, 223, 227, 229, 241, 257, 263, 269, 271, 283, 311, 313, 317, 331, 337, 347, 349, 353, 367, 379, 383, 389, 397, 401, 421, 439, 449, 457, 461, 463, 467, 479, 503, 521
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OFFSET

1,1


COMMENTS

Complement of A087634, primes p such that phi(k) = 4p has a solution, where phi is Euler's totient function.
The sequences a(n), A005384 and A023212 form a partition of the set of primes > 3: Using von StaudtClausen formula the divisors of 4p increased by 1 are {2,3,5,p+1,2p+1,4p+1}, p+1 is clearly an even number, and if 2p+1 and 4p+1 are not prime, then denom(B(4p))=30.  Enrique Pérez Herrero, Aug 15 2011
Also 2 with the primes p such that both 2*p+1 and 4*p+1 are composite: A210684. For these numbers k > 2 the equation: phi(n)=k*tau(n), where phi is A000010 and tau is A000005, has no solutions: A112954(a(n))=0.  Enrique Pérez Herrero, May 12 2012


LINKS

E. Pérez Herrero, Table of n, a(n) for n=1..30000
Wikipedia, Von StaudtClausen theorem


MATHEMATICA

Select[Prime[Range[100]], Denominator[BernoulliB[4# ]]==30&] (* T. D. Noe, Feb 19 2004 *)
Select[Prime[Range[100]], !PrimeQ[4#+1]&&!PrimeQ[2#+1](#==2)&] (* Enrique Pérez Herrero, Aug 16 2011 *)


CROSSREFS

Cf. A051225, A053176, A087634.
Cf. A005384, A023212.
Cf. A210684.
Sequence in context: A153261 A080115 A119480 * A018569 A022118 A041339
Adjacent sequences: A043294 A043295 A043296 * A043298 A043299 A043300


KEYWORD

easy,nonn


AUTHOR

Benoit Cloitre, Mar 24 2002


STATUS

approved



