login
Primes p such that 2*p+1 has exactly three prime factors (not necessarily distinct).
1

%I #26 Nov 10 2022 07:42:47

%S 13,31,37,73,97,103,127,137,139,181,193,199,211,227,241,269,277,307,

%T 313,331,373,379,397,433,457,463,467,541,547,563,571,587,617,619,647,

%U 709,727,733,739,751,757,773,797,829,859,883,887,929,977,1021,1033,1069,1117,1123

%N Primes p such that 2*p+1 has exactly three prime factors (not necessarily distinct).

%H Robert Israel, <a href="/A350409/b350409.txt">Table of n, a(n) for n = 1..10000</a>

%e For p = 31, 2*p+1 = 63, which factors as 3*3*7.

%e For p = 97, 2*p+1 = 195, which factors as 3*5*13.

%p filter:= proc(p) isprime(p) and numtheory:-bigomega(2*p+1)=3 end proc:

%p select(filter, [seq(i,i=3..2000,2)]); # _Robert Israel_, Nov 09 2022

%t Select[Prime@Range@200,PrimeOmega[2#+1]==3&] (* _Giorgos Kalogeropoulos_, Jan 08 2022 *)

%o (PARI) is(n) = bigomega(2*n + 1) == 3 && isprime(n) \\ _David A. Corneth_, Jan 06 2022

%K nonn,easy

%O 1,1

%A _Paul Duckett_, Jan 06 2022

%E More terms from _David A. Corneth_, Jan 06 2022