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.

A124878 Primes in A027612.

Original entry on oeis.org

5, 13, 223, 4861, 197698279, 25472027467, 6975593267347, 218572480850557, 1592457339642613, 2955634782407818711841368777079578319, 2950127241932882597818337002939124083061, 232242878286351670588710938679161483012314573381293769
Offset: 1

Views

Author

Alexander Adamchuk, Nov 11 2006

Keywords

Examples

			A027612(n) begins {1, 5, 13, 77, 87, 223, 481, 4609, 4861, ...}.
Thus a(1) = 5, a(2) = 13, a(3) = 223, a(4) = 4861.

Links

Crossrefs

A027612(n) are the numerators of second order harmonic numbers H(n, (2)).
Corresponding numbers n such that A027612(n) is prime are listed in A124879.
Cf. A001008, A002805, A067657, A056903, A027612, A124879, A124837, A124880, A124881.

Programs

  • Mathematica
    s=1;Do[s=s+1/(n+1);f=Numerator[(n+1)*(s-1)]; If[PrimeQ[f],Print[{n,f}]],{n,1,1942}]
  • PARI
    lista(nn) = {for (n=1, nn, if (isprime(p=numerator(sum(k=1, n, k/(n-k+1)))), print1(p, ", ")););} \\ Michel Marcus, Jul 14 2018

Formula

a(n) = A027612(A124879(n)).

Extensions

a(12) from, and crossrefs edited by Michel Marcus, Jul 14 2018

A124879 Numbers k such that A027612(k) is prime.

Original entry on oeis.org

2, 3, 6, 9, 18, 25, 29, 30, 39, 84, 91, 125, 130, 184, 195, 199, 203, 241, 245, 273, 281, 378, 552, 571, 653, 776, 901, 1099, 1215, 1224, 1235, 1315, 1412, 1657, 1942, 2076, 2085, 2743, 2745, 2855, 2859, 3517, 3717, 4183, 4188, 4362, 4547, 4728, 4783
Offset: 1

Views

Author

Alexander Adamchuk, Nov 11 2006

Keywords

Examples

			A027612 begins {1, 5, 13, 77, 87, 223, 481, 4609, 4861, ...}.
Thus a(1) = 2, a(2) = 3, a(3) = 6, a(4) = 9.

Links

Crossrefs

A027612(n) are the numerators of second order harmonic numbers H(n, (2)).
Corresponding primes in A027612 are listed in A124878.
Cf. A001008, A002805, A067657, A056903, A027612, A124878, A124837, A124880, A124881.

Programs

  • Mathematica
    s=1;Do[s=s+1/(n+1);f=Numerator[(n+1)*(s-1)]; If[PrimeQ[f],Print[{n,f}]],{n,1,1942}]
  • PARI
    isok(n) = isprime(numerator(sum(k=1, n, k/(n-k+1)))); \\ Michel Marcus, Jul 14 2018

Extensions

More terms from Stefan Steinerberger, May 29 2007
Crossrefs edited by Michel Marcus, Jul 14 2018

A124881 Numbers k such that A124837(k) is prime.

Original entry on oeis.org

2, 3, 9, 15, 25, 27, 33, 45, 55, 67, 70, 93, 94, 97, 112, 113, 125, 137, 189, 193, 212, 232, 262, 273, 281, 381, 453, 528, 670, 677, 742, 743, 827, 996, 1257, 1349, 1402, 1645, 1683, 2110, 2217, 2408, 2480, 2623, 3208, 3517, 3637, 3665, 4571, 4730
Offset: 1

Views

Author

Alexander Adamchuk, Nov 11 2006

Keywords

Examples

			A124837(n) begins {1, 7, 47, 57, 459, 341, 3349, 3601, 42131, 44441, ...}.
Thus a(1) = 2, a(2) = 3, a(3) = 9.

Links

Crossrefs

A124837 are the numerators of third-order harmonic numbers H(n, (3)).
Corresponding primes in A124837 are listed in A124880.
Cf. A001008, A002805, A067657, A056903, A027612, A124878, A124879, A124837, A124880.

Programs

  • Mathematica
    s=3/2;Do[s=s+1/n;f=Numerator[n*(n-1)/2*(s-3/2)]; If[PrimeQ[f],Print[{n-2,f}]],{n,3,1000}]

Extensions

More terms from Stefan Steinerberger, May 09 2007
Crossrefs edited by Michel Marcus, Jul 14 2018
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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