A241793 -id:A241793 - cp's OEIS frontend

A242786 Least prime p such that p^n and p^n+1 have the same number of prime factors (counted with multiplicity) or 0 if no such number exists.

2, 3, 3, 43, 7, 41, 23, 643, 17, 557, 251, 13183, 1999, 10007, 107

Offset: 1

Derek Orr, May 22 2014

Also least number k > 1 such that k^n and k^n+1 have the same number of prime factors.
Since the data values are prime, p^n and p^n+1 have n prime factors.
a(21) = 1151.
a(17) = 5119. - Michel Marcus, Sep 21 2018
a(16) > 10^6; a(18) = 33577; a(19) = 48383. - Jon E. Schoenfield, Sep 22 2018
a(20) > 10^6. - Jon E. Schoenfield, Sep 28 2018
a(16) <= 206874667. - Daniel Suteu, Dec 09 2022

			2^3 = 8 and 2^3 + 1 = 9 do not have the same number of prime factors. 3^3 = 27 and 3^3 + 1 = 28 both have 3 prime factors (27 = 3*3*3 and 28 = 7*2*2). Thus, a(3) = 3.

Cf. A001222 (bigomega), A241793.

a(n)=forprime(p=1,oo,if(bigomega(p^n+1)==n,return(p))); \\ Michel Marcus, Sep 21 2018

Data restricted to known terms by Michel Marcus, Sep 21 2018

a(12) & a(14) from Michel Marcus, Sep 21 2018

A368163 a(n) is the smallest number k > 1 such that bigomega(k^n - 1) = n.

Original entry on oeis.org

3, 4, 4, 10, 17, 8, 25, 5, 28, 9, 81, 13, 289, 64, 100, 41, 6561, 31, 6657, 57, 529, 1025

Offset: 1

Daniel Suteu, Dec 14 2023

a(23) <= 196609; a(24) = 79; a(25) <= 28561; a(26) = 14015; a(27) = 961; a(28) = 729; a(30) = 361; a(32) = 2047.

			a(5) = 17 is the smallest number of the set {k(i)} = {17, 19, 21, 26, 27, 39, 45, ...} where k(i)^5 - 1 has exactly 5 prime factors counted with multiplicity.

Cf. A001222, A219019, A241793, A359070.

a(n) = my(k=2); while (bigomega(k^n-1) != n, k++); k;

cp's OEIS Frontend

A242786 Least prime p such that p^n and p^n+1 have the same number of prime factors (counted with multiplicity) or 0 if no such number exists.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI

Extensions