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Search: id:A092194
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| A092194 |
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Primes p that divide A001008(k), the numerator of the k-th harmonic number H(k), for some k < p-1. |
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+0
3
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| 11, 29, 37, 43, 53, 61, 97, 109, 137, 173, 199, 227, 257, 269, 271, 313, 347, 353, 379, 397, 401, 409, 421, 433, 439, 509, 521, 577, 599, 601, 617, 641, 643, 647, 659, 677, 733, 761, 773, 809, 821, 827, 839, 863, 911, 919, 929, 937, 941, 947, 953, 971, 1009
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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These primes are a subset of the non-harmonic primes A092102. Because these primes are analogous to the irregular primes A000928 that divide the numerators of Bernoulli numbers, they might be called H-irregular primes. The density of these primes is about 0.4 -- very close to the density of irregular primes.
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LINKS
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Eric Weisstein's World of Mathematics, Harmonic Number
Eric Weisstein's World of Mathematics, Irregular Prime
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MATHEMATICA
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n=2; Table[cnt=0; While[cnt==0, p=Prime[n]; k=1; h=0; While[cnt==0 && k<=(p-1)/2, h=h+1/k; If[Mod[Numerator[h], p]==0, cnt++ ]; k++ ]; n++ ]; p, {100}]
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CROSSREFS
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Cf. A072984 (least k such that prime(n) divides A001008(k)).
Sequence in context: A126240 A124110 A153768 this_sequence A134307 A087693 A106017
Adjacent sequences: A092191 A092192 A092193 this_sequence A092195 A092196 A092197
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Feb 24 2004
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