A360549 - OEIS

%I #33 Mar 06 2023 02:55:11

%S 2,43,7,5,3,17,11,19,23,29,13,31,37,41,61,53,71,59,79,103,67,47,83,89,

%T 97,73,101,137,107,131,113,109,127,139,151,167,149,173,181,157,197,

%U 191,163,193,211,199,227,179,223,229,241,233,349,257,251,283,307,271,263,293,281,317,239,269,313

%N a(n) is the least prime p not already in the sequence such that a(n-1) + p is a triprime; a(1) = 2.

%C Conjecture: every prime eventually appears in the sequence.

%H Robert Israel, <a href="/A360549/b360549.txt">Table of n, a(n) for n = 1..10000</a>

%e a(4) = 5 because 5 is a prime that has not yet occurred in the sequence, a(4) + 5 = 12 = 2^2^3 is a triprime; the only other prime (3) that has not yet occurred does not work because a(4) + 3 = 10 = 2*5 is not a triprime.

%p R:= 2: p:= 2: P:= select(isprime, [seq(i,i=3..10000,2)]):

%p do

%p   found:= false;

%p   for k from 1 to nops(P) do

%p       q:= P[k];

%p       if numtheory:-bigomega(q+p) = 3 then

%p       found:= true; p:= q; R:= R,p; P:= subsop(k=NULL,P); break

%p     fi

%p   od;

%p   if not found then break fi;

%p od:

%p R;

%Y Cf. A014612, A353408.

%K nonn

%O 1,1

%A _Zak Seidov_ and _Robert Israel_, Mar 04 2023