cp's OEIS Frontend

A333747 Numbers that are either the product of two consecutive primes or two primes with a prime in between.

%I A333747 #61 Jan 19 2023 22:48:27
%S A333747 6,10,15,21,35,55,77,91,143,187,221,247,323,391,437,551,667,713,899,
%T A333747 1073,1147,1271,1517,1591,1763,1927,2021,2279,2491,2773,3127,3233,
%U A333747 3599,3953,4087,4331,4757,4891,5183,5609,5767,6059,6557,7031,7387,8051,8633,8989,9797,9991
%N A333747 Numbers that are either the product of two consecutive primes or two primes with a prime in between.
%C A333747 In other words, these are numbers that are the product of two distinct primes whose prime indices differ by at most two.
%H A333747 Robert Israel, <a href="/A333747/b333747.txt">Table of n, a(n) for n = 1..10000</a>
%F A333747 Union of A006094 and A090076.
%F A333747 a(n) = prime(ceiling(n/2))*prime(ceiling((n+3)/2)).
%F A333747 a(2*n-1) = prime(n)*prime(n+1).
%F A333747 a(2*n) = prime(n)*prime(n+2).
%p A333747 R:= NULL;
%p A333747 p:= 2; q:= 3;
%p A333747 for n from 1 to 100 by 2 do
%p A333747   r:= nextprime(q);
%p A333747   R:= R, p*q, p*r;
%p A333747   p:= q; q:= r;
%p A333747 od:
%p A333747 R; # _Robert Israel_, Apr 22 2020
%t A333747 a[n_] := Prime[Ceiling[n/2]] * Prime[Ceiling[(n + 3)/2]]; Array[a, 50] (* _Amiram Eldar_, Apr 04 2020 *)
%Y A333747 Subsequence of A001358.
%Y A333747 Cf. A000040, A006094, A090076, A110654, A332765, A332877.
%K A333747 nonn,easy
%O A333747 1,1
%A A333747 _Bobby Jacobs_, Apr 03 2020