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 1-4 of 4 results.

A239736 Least k > 0 such that p(n)+p(k)-1 is prime, where p(n) is the number of partitions of n.

Original entry on oeis.org

1, 1, 1, 1, 1, 3, 2, 2, 2, 10, 3, 1, 3, 8, 3, 6, 4, 2, 4, 9, 9, 4, 4, 8, 2, 2, 2, 3, 11, 8, 4, 13, 19, 4, 1, 6, 3, 4, 2, 4, 26, 12, 5, 11, 11, 9, 6, 5, 25, 4, 24, 6, 4, 2, 5, 9, 9, 2, 7, 4, 28, 13, 8, 27, 9, 23, 3, 7, 2, 24, 36, 38, 9, 26, 16, 1
Offset: 2

Views

Author

Sean A. Irvine, Mar 25 2014

Keywords

Comments

Conjecture of Zhi-Wei Sun: a(n) < n for n > 1.

Examples

			a(7)=3, since p(7)+p(1)-1=15 and p(7)+p(2)-1=16 are composite, but p(7)+p(3)-1=17 is prime.

Links

Crossrefs

Cf. A000040, A000041, A239675.

Programs

  • Mathematica
    a[n_] := For[k = 1, True, k++, If[PrimeQ[PartitionsP[n] + PartitionsP[k] - 1], Return[k]]];
Table[a[n], {n, 2, 100}] (* Jean-François Alcover, Dec 12 2018 *)
  • PARI
    s=[]; for(n=2, 100, k=1; while(!isprime(numbpart(n)+numbpart(k)-1), k++); s=concat(s, k)); s \\ Colin Barker, Mar 26 2014

A240545 Least k > 0 such that n + p(k) is prime, where p(k) is the number of partitions of k.

Original entry on oeis.org

2, 1, 1, 2, 1, 2, 1, 8, 3, 2, 1, 2, 1, 9, 3, 2, 1, 2, 1, 8, 3, 2, 1, 9, 4, 8, 3, 2, 1, 2, 1, 8, 4, 11, 3, 2, 1, 8, 3, 2, 1, 2, 1, 9, 3, 2, 1, 10, 4, 8, 3, 2, 1, 9, 4, 10, 3, 2, 1, 2, 1, 8, 4, 15, 3, 2, 1, 8, 3, 2, 1, 2, 1, 9, 4, 8, 3, 2, 1, 8, 3, 2
Offset: 0

Views

Author

Sean A. Irvine, Apr 07 2014

Keywords

Comments

Conjecture of Zhi-Wei Sun: a(n) < n for n > 7.
Verified up to 6*10^8. - Sean A. Irvine, Apr 07 2014

Examples

			a(7)=8 because k=8 is the smallest k such that 7+A000041(k) is prime.

Links

Crossrefs

Cf. A000040, A000041, A238457, A239675.

Programs

  • Mathematica
    a[n_] := For[k = 1, True, k++, If[PrimeQ[n + PartitionsP[k]], Return[k]]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Dec 15 2018 *)

A239701 Least k > 0 such that q(n)+k is prime, where q(n) is the number of strict partitions of n.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 1, 2, 1, 1, 2, 5, 3, 1, 5, 3, 3, 8, 3, 5, 7, 2, 1, 1, 1, 11, 7, 7, 1, 9, 2, 5, 1, 13, 1, 4, 17, 1, 3, 7, 5, 5, 1, 7, 7, 1, 2, 1, 27, 19, 1, 1, 2, 11, 11, 3, 21, 3, 3, 3, 11, 11, 9, 17, 13, 20, 1, 1, 5, 7, 3, 17, 12
Offset: 0

Views

Author

Sean A. Irvine, Mar 24 2014

Keywords

Comments

Conjecture of Zhi-Wei Sun: a(n) <= n for n > 0.

Links

Crossrefs

Cf. A000009, A000040, A239675.

Programs

  • Mathematica
    a[n_] := For[k = 1, True, k++, If[PrimeQ[PartitionsQ[n] + k], Return[k]]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Feb 19 2019 *)

A239936 Least k > 0 such that p(k)+q(n) is prime, where p(n) is the number of partitions of n and q(n) is the number of strict partitions of n.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 1, 2, 1, 1, 2, 4, 3, 1, 4, 3, 3, 10, 3, 4, 5, 2, 1, 1, 1, 6, 5, 5, 1, 6, 2, 4, 1, 12, 1, 15, 13, 1, 3, 5, 4, 4, 1, 5, 5, 1, 2, 1, 12, 49, 1, 1, 2, 6, 6, 3, 14, 3, 3, 3, 6, 6, 16, 13, 16, 11, 1, 1, 4, 5, 3, 12, 25
Offset: 0

Views

Author

Sean A. Irvine, Mar 29 2014

Keywords

Comments

Conjecture of Zhi-Wei Sun: a(n) < n for n > 1.

Examples

			a(5)=2 since q(5)+p(2)=3+2=5 is prime but q(5)+p(1)=4 is composite.

Links

Crossrefs

Cf. A000009, A000040, A000041, A239675, A239736.

Programs

  • Mathematica
    a[n_] := For[k = 1, True, k++, If[PrimeQ[PartitionsP[k] + PartitionsQ[n]], Return[k]]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Feb 19 2019 *)
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.