

A092101


Harmonic primes.


10



5, 13, 17, 23, 41, 67, 73, 79, 107, 113, 139, 149, 157, 179, 191, 193, 223, 239, 241, 251, 263, 277, 281, 293, 307, 311, 317, 331, 337, 349, 431, 443, 449, 461, 467, 479, 487, 491, 499, 503, 541, 547, 557, 563, 569, 593, 619, 653, 683, 691, 709, 757, 769, 787
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OFFSET

1,1


COMMENTS

For p = prime(n), Boyd defines J_p to be the set of numbers k such that p divides A001008(k), the numerator of the harmonic number H(k). For harmonic primes, J_p contains only the three numbers p1, (p1)p and (p1)(p+1). It has been conjectured that there are an infinite number of these primes and that their density in the primes is 1/e.
Prime p=A000040(n) is in this sequence iff neither H(k) == 0 (mod p), nor H(k) == A177783(n) (mod p) have solutions for 1 <= k <= p2.  Max Alekseyev, May 13 2010


LINKS



PROG

(PARI) is(p)=my(K=Mod((binomial(2*p1, p)1)/2/p^3, p), H=Mod(0, p)); for(k=1, p2, H+=1/k; if(H==0H==K, return(0))); 1 \\ Charles R Greathouse IV, Mar 16 2014


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



