A348017 Numbers k such that the numerator of the fractional part of the k-th harmonic is a prime number.

3, 5, 7, 9, 10, 12, 19, 21, 24, 29, 34, 39, 45, 46, 54, 65, 84, 86, 116, 128, 161, 177, 248, 254, 274, 297, 349, 352, 412, 422, 475, 493, 636, 747, 793, 811, 855, 864, 1012, 1060, 1074, 1097, 1127, 1139, 1152, 1299, 1371, 1423, 1785, 1847, 1872, 1873, 2072, 2326

Offset

1,1

Comments

The corresponding primes are 5, 17, 83, 2089, 2341, 2861, 42503239, 3338549, 276977179, 2239777822987, ...

Links

Amiram Eldar, Table of n, a(n) for n = 1..96

Example

3 is a term since 1 + 1/2 + 1/3 = 11/6, the fractional part of 11/6 is 5/6 and its numerator, 5, is prime.
5 is a term since 1 + 1/2 + 1/3 + 1/4 + 1/5 = 137/60, the fractional part of 137/60 is 17/60 and its numerator, 17, is prime.

Mathematica

s = 0; seq = {}; Do[s += 1/n; If[PrimeQ @ Numerator @ FractionalPart[s], AppendTo[seq, n]], {n, 1, 2500}]; seq

Prog

(Python)
from sympy import harmonic, isprime
A348017_list = [k for k in range(10**3) if isprime((lambda x: x.p % x.q)(harmonic(k)))] # Chai Wah Wu, Sep 26 2021

Crossrefs

Cf. A056903, A104174.

Sequence in context: A294601 A358529 A080207 * A187347 A187413 A091177

Adjacent sequences: A348014 A348015 A348016 * A348018 A348019 A348020

Keyword

nonn

Author

Amiram Eldar, Sep 24 2021

Status

approved