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 1-2 of 2 results.

A088076 Smallest prime sandwiched between two numbers having exactly n prime divisors.

Original entry on oeis.org

3, 11, 131, 1429, 77141, 3847271, 117048931, 22917541219, 1771365487891, 140734085123059, 14159733947566481
Offset: 1

Views

Author

Amarnath Murthy, Sep 22 2003

Keywords

Comments

Different from A088075 though initial three terms match. Sequence is infinite.

Examples

			a(3) = 131, 130 = 2*5*13 and 132 = 2^2*3*11 both have three prime divisors. 131 is the smallest such prime.

References

  • J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 131, p. 45, Ellipses, Paris 2008.

Crossrefs

Cf. A088075.

Extensions

More terms from Ray Chandler, Oct 08 2003
a(8) and a(9) from Donovan Johnson, Jun 19 2008
a(10)-a(11) from Donovan Johnson, Feb 18 2009

A365326 a(n) is the smallest positive number k such that k^2 - 1 and k^2 + 1 each have exactly n distinct prime divisors.

Original entry on oeis.org

2, 5, 13, 83, 463, 4217, 169333, 2273237, 23239523, 512974197, 5572561567
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Sep 01 2023

Keywords

Crossrefs

Cf. A001221, A180278, A219017.
Cf. A088075 (with k instead of k^2).

Programs

  • PARI
    isok(k, n) = (omega(k^2-1)==n) && (omega(k^2+1)==n);
a(n) = my(k=2); while (!isok(k, n), k++); k; \\ Michel Marcus, Sep 03 2023

Formula

a(n) >= max(A219017(n), A180278(n)). - Daniel Suteu, Sep 03 2023

Extensions

a(9)-a(11) from Amiram Eldar, Sep 03 2023
Showing 1-2 of 2 results.

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