

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

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
David W. Boyd, A padic study of the partial sums of the harmonic series, Experimental Math., Vol. 3 (1994), No. 4, 287302.
A. Eswarathasan and E. Levine, pintegral harmonic sums, Discrete Math. 91 (1991), 249257.


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

Cf. A092102 (nonharmonic primes), A092103 (size of J_p).
Sequence in context: A182078 A074278 A087895 * A105596 A037046 A126887
Adjacent sequences: A092098 A092099 A092100 * A092102 A092103 A092104


KEYWORD

nonn


AUTHOR

T. D. Noe, Feb 20 2004


EXTENSIONS

More terms from Max Alekseyev, May 13 2010


STATUS

approved



