|
%I #10 Apr 27 2022 18:36:19
%S 22,51,145,287,1717,2147,3151,5017,11051,13207,16801,20827,26867,
%T 63551,68587,71177,76501,96647,112477,147737,159251,232657,237407,
%U 308947,314417,342487,433897,480251,587501,602617,722107,772927,834401,861467,879751,907537,945257,1155887,1177051
%N Semiprimes of the form p(6p - 1).
%H Harvey P. Dale, <a href="/A330409/b330409.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A049452(A158015(n)) = p(6p - 1) with p = A158015(n).
%e A158015(1) = 2 is the smallest prime p such that 6p - 1 = 12 - 1 = 11 is also prime, whence a(1) = A049452(2) = 2*(6*2 - 1) = 22.
%e prime(5) = 11 is the smallest prime not in A024898 or A158015, because 6p - 1 is not a prime, therefore A049452(11) = 11*(6*11 - 1) is not in the sequence, and idem for A049452(13).
%e But prime(7) = 17 is in A024898 and A158015, so a(5) = A024898(A158015(5)) = A024898(17) = 17*(6*17 - 1).
%t Select[Table[p(6p-1),{p,500}],PrimeOmega[#]==2&] (* _Harvey P. Dale_, Apr 27 2022 *)
%o (PARI) [p*(6*p-1) | p<-primes(99), isprime(6*p-1)]
%Y Cf. A024898 (6n-1 is prime), A158015 (primes), A049452 = {n(6n-1)}.
%Y Complement of A255584 = A033570(A130800) (semiprimes (2n+1)(3n+1)) in A245365 (primes of the form n(3n-1)/2).
%K nonn
%O 1,1
%A _M. F. Hasler_, Dec 13 2019
|
