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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 (list; graph; refs; listen; history; text; internal format)
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 p-1, (p-1)p and (p-1)(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 <= p-2. - Max Alekseyev, May 13 2010
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
David W. Boyd, A p-adic study of the partial sums of the harmonic series, Experimental Math., Vol. 3 (1994), No. 4, 287-302.
A. Eswarathasan and E. Levine, p-integral harmonic sums, Discrete Math. 91 (1991), 249-257.
PROG
(PARI) is(p)=my(K=-Mod((binomial(2*p-1, p)-1)/2/p^3, p), H=Mod(0, p)); for(k=1, p-2, H+=1/k; if(H==0||H==K, return(0))); 1 \\ Charles R Greathouse IV, Mar 16 2014
CROSSREFS
Cf. A092102 (non-harmonic primes), A092103 (size of J_p).
Sequence in context: A182078 A074278 A087895 * A105596 A037046 A126887
KEYWORD
nonn
AUTHOR
T. D. Noe, Feb 20 2004
EXTENSIONS
More terms from Max Alekseyev, May 13 2010
STATUS
approved

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Last modified May 26 05:37 EDT 2024. Contains 372807 sequences. (Running on oeis4.)