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

Author

Derek Orr, May 22 2014

Keywords

• nonn
• more
• hard

Comments

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

Examples

			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.
		

Crossrefs

Cf. A001222 (bigomega), A241793.

Programs

PARI

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

Extensions

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

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