cp's OEIS Frontend

A367855 The slowest increasing sequence of semiprimes such that a(n-1) + a(n) is prime.

%I A367855 #9 Dec 03 2023 01:55:43
%S A367855 4,9,10,21,22,25,34,39,58,69,82,85,94,129,134,143,194,203,206,213,218,
%T A367855 221,278,291,302,305,314,327,334,339,362,365,386,411,446,473,566,597,
%U A367855 626,633,674,687,694,745,766,793,1018,1081,1126,1141,1198,1219,1402,1417,1486,1513,1654,1689,1718,1731
%N A367855 The slowest increasing sequence of semiprimes such that a(n-1) + a(n) is prime.
%C A367855 a(2*n) is odd and a(2*n-1) is twice a prime where n is a positive integer. - _David A. Corneth_, Dec 03 2023
%H A367855 Robert Israel, <a href="/A367855/b367855.txt">Table of n, a(n) for n = 1..10000</a>
%e A367855 a(4) = 21 because a(3) = 10, 21 = 3 * 7 is a semiprime > 10, 10 + 21 = 31 is prime, and no smaller semiprime > 10 works.
%p A367855 R:= 4: s:= 4:
%p A367855 for count from 2 to 100 do
%p A367855   for t from s+1 by 2 do
%p A367855     if isprime(s+t) and numtheory:-bigomega(t) = 2 then
%p A367855       R:= R,t; s:= t; break
%p A367855     fi
%p A367855   od
%p A367855 od:
%p A367855 R;
%t A367855 s = {q = 4}; Do[p = q + 1; While[ PrimeOmega[p] != 2, p = p + 2]; AppendTo[s, q = p], {120}]; s
%Y A367855 Cf. A001358, A116656, A126938.
%K A367855 nonn
%O A367855 1,1
%A A367855 _Zak Seidov_ and _Robert Israel_, Dec 02 2023