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A126225 Least number k > 0 such that the numerator of Sum_{i=1..k} 1/prime(i)^n is a prime. 0
2, 2, 3, 2, 3, 5, 3, 11, 3, 22 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(12) > 80, a(13) = 30, a(14) = 16, a(18) = 7, a(19) = 3. - J. Mulder (jasper.mulder(AT)planet.nl), Jan 25 2010

a(11) > 200, a(12) > 200. - Michel Marcus, May 27 2019

LINKS

Table of n, a(n) for n=1..10.

EXAMPLE

a(1) = 2 corresponds to A024451(2) = 5, a prime.

a(2) = 2 corresponds to A061015(2) = 13, a prime.

MATHEMATICA

a[n_] := Block[{i = 1, sum = 0}, While[True, sum += 1/Prime[i]^n; If[PrimeQ[Numerator@sum], Return[i]]; i++ ]] (* J. Mulder (jasper.mulder(AT)planet.nl), Jan 25 2010 *)

PROG

(PARI) a(n) = {my(k=1, s=1/prime(k)^n); while (! isprime(numerator(s)), k++; s += 1/prime(k)^n); k; } \\ Michel Marcus, May 27 2019

CROSSREFS

Cf. A024451 (1/p), A061015 (1/p^2), A115963 (1/p^3).

Sequence in context: A037126 A080092 A164738 * A306997 A056160 A106245

Adjacent sequences:  A126222 A126223 A126224 * A126226 A126227 A126228

KEYWORD

hard,more,nonn

AUTHOR

Alexander Adamchuk, Mar 08 2007

STATUS

approved

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Last modified September 20 06:51 EDT 2020. Contains 337264 sequences. (Running on oeis4.)