A364442 - OEIS

%I #8 Aug 02 2023 13:48:29

%S 1,7,11,16,26,37,38,40,52,53,57,59,65,73,74,79,85,86,88,94,96,99,108,

%T 114,116,120,122,123,132,134,139,140,142,143,147,163,169,174,180,183,

%U 186,188,197,202,204,206,212,213,215,219,223,229,236,238,239,244,250,256,262,268,271,277,278,283

%N a(n) is the smallest number > a(n-1) such that a(n-1) + a(n) is a triprime (A014612), with a(1) = 1.

%C For n > 1, a(n) is the least number > a(n-1) such that A001222(a(n) + a(n-1)) = 3.

%C a(n-1) + a(n) is the least triprime > 2*a(n-1).

%H Robert Israel, <a href="/A364442/b364442.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 11 because a(2) = 7, none of 7 + 8 = 15, 7 + 9 = 16 and 7 + 10 = 17 is a triprime, but 7 + 11 = 18 = 2*3^2 is a triprime.

%p R:= 1: x:= 1:

%p for i from 1 to 100 do

%p    for y from x+1 while numtheory:-bigomega(x+y) <> 3 do od:

%p    R:= R,y;

%p    x:= y

%p od:

%p R;

%t s = {p = 1}; Do[q = p + 1; While[3 != PrimeOmega[p + q],

%t q++];  AppendTo[s, p = q], {100}]; s

%Y Cf. A001222, A014612, A073627, A263349, A357713.

%K nonn

%O 1,2

%A _Zak Seidov_ and _Robert Israel_, Jul 25 2023