cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A165132 Primes whose logarithms are known to possess ternary BBP formulas.

Original entry on oeis.org

2, 3, 5, 7, 11, 13
Offset: 1

Views

Author

Jaume Oliver Lafont, Sep 04 2009

Keywords

Comments

From Jaume Oliver Lafont, Oct 07 2009: (Start)
log(2)=(2/3)P(1,9,2,(1,0))
log(3)=(1/9)P(1,9,2,(9,1))
log(5)=(4/27)P(1,3^4,4,(9,3,1,0))
log(7)=(1/3^5)P(1,3^6,6,(405,81,72,9,5,0))
log(11)=(1/(2*3^9))P(1,3^10,10,(85293,10935,9477,1215,648,135,117,15,13,0))
log(13)=(1/3^5)P(1,3^6,6,(567,81,36,9,7,0))
See the link for the definition of P notation.
Equivalent expressions in reduced coefficients are given in the code section.
(End)

Links

Crossrefs

Cf. A104885.

Programs

  • PARI
    \\ Jaume Oliver Lafont, Oct 07 2009
log2=2*suminf(k=1,[0,1][k%2+1]/k/3^k)
log3=suminf(k=1,[1,3][k%2+1]/k/3^k)
log5=4*suminf(k=1,[0,1,1,1][k%4+1]/k/3^k)
log7=suminf(k=1,[0,5,3,8,3,5][k%6+1]/k/3^k)
log11=suminf(k=1,[0,13,5,13,5,8,5,13,5,13][k%10+1]/k/3^k)/2
log13=suminf(k=1,[0,7,3,4,3,7][k%6+1]/k/3^k)

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...

Original entry on oeis.org

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

Views

Author

Stefan Krämer, Sep 01 2005

Keywords

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

Crossrefs

Cf. A104885, A109997.
Cf. A153810 (1-gamma).

Programs

  • 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 *)
  • 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

A109997 Primes where the arithmetic mean of the fractional parts of p/1,p/2,..., p/p is less than 1-gamma=0.422784...

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 29, 31, 37, 41, 43, 61, 67, 73, 79, 97, 101, 103, 109, 113, 127, 137, 151, 157, 163, 173, 181, 193, 197, 199, 211, 229, 233, 241, 257, 271, 277, 281, 283, 307, 313, 331, 337, 353, 367, 373, 379, 397, 401, 409, 421, 433, 443, 457, 463
Offset: 1

Views

Author

Stefan Krämer, Sep 01 2005

Keywords

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

Crossrefs

Cf. A104885, A109996.

Programs

  • Mathematica
    With[{c=1-EulerGamma},Select[Prime[Range[100]],Mean[FractionalPart/@(#/ Range[#])]Harvey P. Dale, Sep 19 2020 *)
Showing 1-3 of 3 results.

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