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.

A248891 Number of primes p such that p+2 is prime and A001359(n) < p < A001359(n)^(1+1/n).

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 2, 2, 3, 2, 4, 3, 4, 4, 3, 4, 3, 3, 2, 1, 2, 3, 2, 2, 5, 4, 3, 2, 1, 1, 4, 3, 2, 3, 4, 6, 5, 4, 3, 4, 5, 6, 7, 6, 5, 4, 5, 5, 5, 4, 5, 4, 5, 5, 5, 6, 9, 8, 8, 7, 7, 7, 8, 7, 6, 6, 5, 4, 3, 3, 3, 2, 7, 6, 5, 5, 5, 4, 3, 2, 5, 5, 8, 9, 11, 10, 10, 9, 9, 8, 7, 7, 6, 6, 6, 5, 4, 5, 8, 8
Offset: 1

Views

Author

Jahangeer Kholdi and Farideh Firoozbakht, Nov 22 2014

Keywords

Comments

Conjecture: For every positive integer n, A001359(n+1)^(1/(n+1)) < A001359(n)^(1/n). Note that this conjecture is equivalent to " A001359 is infinite and for every n, A001359(n+1) < A001359(n)^(1+1/n). This implies for every n, a(n) is positive. See comment lines of the sequence A001359.

Examples

			Take n=1, A001359(1)=3, 3 < 5 < 3^(1+1/1)=9 hence a(1)=1.
Take n=6, A001359(6)=41, 41 < 59 < 71 < 41^(1+1/6)~76.13 hence a(6)=2.

Crossrefs

Cf. A001359, A248901, A248902, A248903.

A248903 Numbers k such that A248891(k) = 3.

Original entry on oeis.org

9, 12, 15, 17, 18, 22, 27, 32, 34, 39, 69, 70, 71, 79, 128, 143, 172, 226, 241, 242, 248, 269, 322, 325, 403, 405, 406, 420, 745, 2057, 2272, 2606, 2607, 3339, 3340, 3562, 4116, 4117, 4446, 5985, 6834, 7116, 7117, 7490, 7669, 13386, 13388, 15148, 15149, 15150
Offset: 1

Views

Author

Jahangeer Kholdi and Farideh Firoozbakht, Nov 22 2014

Keywords

Comments

Sequence A248894 gives terms a(n) such that a(n+1)=a(n)+1.

Links

Crossrefs

Cf. A001359, A248891, A248894, A248901, A248902.

Programs

  • PARI
    lista(nn) = {my(c=q=0, r, v=List([3, 5, 11, 17])); forprime(p=19, nn, if(p-2==q, listput(v,q); if((t=v[c++]^(1+1/c))>v[c+3] && tJinyuan Wang, Nov 28 2020

A248901 Numbers k such that A248891(k) = 1.

Original entry on oeis.org

1, 2, 3, 4, 5, 20, 29, 30, 2059, 5987, 7119, 20165, 151819, 14984624, 105181798
Offset: 1

Views

Author

Jahangeer Kholdi and Farideh Firoozbakht, Nov 22 2014

Keywords

Comments

If k is in {1, 2, 3, 4, 29, ...} then both numbers k and k+1 are in the sequence.

Crossrefs

Cf. A001359, A248891, A248902, A248903.

Programs

  • PARI
    lista(nn) = {my(c=0, q=r=5, s=3, t); forprime(p=9, nn, if(p-2==q, if((t=s^(1+1/c++))>r && tJinyuan Wang, Nov 28 2020

Extensions

a(13)-a(15) from Jinyuan Wang, Nov 28 2020
Showing 1-3 of 3 results.

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

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