A109996 Primes p such that the arithmetic mean of the fractional parts of p/1, p/2, ..., p/p is larger than 1 - gamma = 0.422784...

23, 47, 53, 59, 71, 83, 89, 107, 131, 139, 149, 167, 179, 191, 223, 227, 239, 251, 263, 269, 293, 311, 317, 347, 349, 359, 383, 389, 419, 431, 439, 449, 461, 467, 479, 491, 503, 509, 557, 569, 571, 587, 593, 599, 607, 619, 643, 647, 659, 683, 701, 719, 727

Offset

1,1

References

S. R. Finch. Mathematical Constants. Cambridge University Press, 2003 ISBN 0-521-81802-2 p. 29.

Stefan Kraemer. Eulers constant and related numbers, preprint, 2005.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Stefan Kraemer, Euler's Constant 0.577... Its Mathematics and History

Maple

H:= proc(n) H(n):= 1/n+`if`(n=1, 0, H(n-1)) end:
a:= proc(n) option remember; local c, p; Digits := 1000;
      c:= evalf(1-gamma);
      p:=`if`(n=1, 1, a(n-1));
      do p:= nextprime(p);
         if H(p)-add(iquo(p, i), i=1..p)/p>c
         then return p fi
      od
    end:
seq(a(n), n=1..70);  # Alois P. Heinz, Jun 14 2013

Mathematica

Reap[For[p = 2, p < 1000, p = NextPrime[p], If[Mean[FractionalPart /@ (p/Range[p])] > 1-EulerGamma, Sow[p]]]][[2, 1]] (* Jean-François Alcover, Dec 28 2021 *)

Prog

(PARI) lista(nn) = {forprime(p=2, nn, if (sum (i=1, p, p/i - floor(p/i))/p > 1- Euler, print1(p, ", ")); ); } \\ Michel Marcus, Jun 14 2013

Crossrefs

Cf. A104885, A109997.

Cf. A153810 (1-gamma).

Sequence in context: A344133 A103629 A253177 * A188833 A121762 A185935

Adjacent sequences: A109993 A109994 A109995 * A109997 A109998 A109999

Keyword

nonn

Author

Stefan Krämer, Sep 01 2005

Status

approved