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

6, 10, 15, 21, 35, 55, 77, 91, 143, 187, 221, 247, 323, 391, 437, 551, 667, 713, 899, 1073, 1147, 1271, 1517, 1591, 1763, 1927, 2021, 2279, 2491, 2773, 3127, 3233, 3599, 3953, 4087, 4331, 4757, 4891, 5183, 5609, 5767, 6059, 6557, 7031, 7387, 8051, 8633, 8989, 9797, 9991

Offset: 1

Author

Bobby Jacobs, Apr 03 2020

Keywords

• nonn
• easy

Comments

In other words, these are numbers that are the product of two distinct primes whose prime indices differ by at most two.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A001358.

Cf. A000040, A006094, A090076, A110654, A332765, A332877.

Programs

Maple

R:= NULL;
p:= 2; q:= 3;
for n from 1 to 100 by 2 do
  r:= nextprime(q);
  R:= R, p*q, p*r;
  p:= q; q:= r;
od:
R; # Robert Israel, Apr 22 2020

Mathematica

a[n_] := Prime[Ceiling[n/2]] * Prime[Ceiling[(n + 3)/2]]; Array[a, 50] (* Amiram Eldar, Apr 04 2020 *)

Formula

Union of A006094 and A090076.

a(n) = prime(ceiling(n/2))*prime(ceiling((n+3)/2)).

a(2*n-1) = prime(n)*prime(n+1).

a(2*n) = prime(n)*prime(n+2).