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%I #30 Dec 10 2022 01:27:39
%S 2,3,3,43,7,41,23,643,17,557,251,13183,1999,10007,107
%N 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.
%C Also least number k > 1 such that k^n and k^n+1 have the same number of prime factors.
%C Since the data values are prime, p^n and p^n+1 have n prime factors.
%C a(21) = 1151.
%C a(17) = 5119. - _Michel Marcus_, Sep 21 2018
%C a(16) > 10^6; a(18) = 33577; a(19) = 48383. - _Jon E. Schoenfield_, Sep 22 2018
%C a(20) > 10^6. - _Jon E. Schoenfield_, Sep 28 2018
%C a(16) <= 206874667. - _Daniel Suteu_, Dec 09 2022
%e 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.
%o (PARI) a(n)=forprime(p=1,oo,if(bigomega(p^n+1)==n,return(p))); \\ _Michel Marcus_, Sep 21 2018
%Y Cf. A001222 (bigomega), A241793.
%K nonn,more,hard
%O 1,1
%A _Derek Orr_, May 22 2014
%E Data restricted to known terms by _Michel Marcus_, Sep 21 2018
%E a(12) & a(14) from _Michel Marcus_, Sep 21 2018