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 A056903 Numbers n such that the numerator of the rational number 1 + 1/2 + 1/3 + ... + 1/n is a prime number. 13
 2, 3, 5, 8, 9, 21, 26, 41, 56, 62, 69, 79, 89, 91, 122, 127, 143, 167, 201, 230, 247, 252, 290, 349, 376, 459, 489, 492, 516, 662, 687, 714, 771, 932, 944, 1061, 1281, 1352, 1489, 1730, 1969, 2012, 2116, 2457, 2663, 2955, 3083, 3130, 3204, 3359, 3494, 3572 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Related to partial sums of the harmonic series and to Wolstenholme's Theorem. Some of the larger entries may only correspond to probable primes. LINKS Eric Weisstein, Table of n, a(n) for n = 1..97 J. Sondow and E. W. Weisstein, MathWorld: Harmonic Number Eric Weisstein's World of Mathematics, Integer Sequence Primes EXAMPLE 5 is in this sequence because 1+1/2+1/3+1/4+1/5 = 137/60 and 137 is prime. MATHEMATICA Select[Range[1000], PrimeQ[Numerator[HarmonicNumber[ # ]]] &] PROG (Perl) use ntheory ":all"; for (1..1000) { say if is_prime((harmfrac(\$_))[0]); } # Dana Jacobsen, Feb 05 2016 (PARI) isok(n) = isprime(numerator(sum(k=1, n, 1/k))); \\ Michel Marcus, Feb 05 2016 CROSSREFS Cf. A002387, A004080. Cf. A001008 (numerator of the harmonic number H(n)), A067657 (primes that are the numerator of a harmonic number). Sequence in context: A120057 A099422 A294913 * A229139 A293277 A331864 Adjacent sequences: A056900 A056901 A056902 * A056904 A056905 A056906 KEYWORD nonn AUTHOR James R. Buddenhagen, Feb 23 2001 EXTENSIONS Terms from 201 to 492 computed by Jud McCranie. More terms from Kamil Duszenko (kdusz(AT)wp.pl), Jun 22 2003 29 more terms from T. D. Noe, Sep 15 2004 Further terms found by Eric W. Weisstein, Mar 07 2005, Mar 29 2005, Nov 28 2005, Sep 23 2006 STATUS approved

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Last modified February 5 03:20 EST 2023. Contains 360082 sequences. (Running on oeis4.)