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%I #12 Mar 05 2023 03:13:12
%S 2,7,3,11,23,59,47,71,107,167,131,83,179,347,191,263,239,227,251,311,
%T 383,419,359,443,479,503,431,467,491,647,587,599,683,719,563,743,659,
%U 827,887,839,983,911,863,1019,947,1091,971,1151,1031,1163,1223,1103,1259,1187,1367,1451,1283,1319,1427,1307,1439,1523,1499
%N a(n) is the least new prime number such that a(n) + a(n-1) is a semiprime.
%C Starting with a(3) = 3, (a(n) + a(n-1))/2 is a prime.
%C For n >= 4, a(n) == 11 (mod 12). Conjecture: every prime == 11 (mod 12) occurs in the sequence. - _Robert Israel_, Mar 04 2023
%H Robert Israel, <a href="/A353408/b353408.txt">Table of n, a(n) for n = 1..10000</a>
%e 2+7=9=3*3, 7+3=10=2*5, 3+11=14=2*7 are all semiprimes.
%p R:= 2,7: p:= 7: P:= select(isprime, [3,seq(i,i=11..2000,12)]):
%p nP:= nops(P): count:= 2:
%p do
%p found:= false;
%p for k from 1 to nops(P) do
%p q:= P[k];
%p if isprime((p+q)/2) then
%p found:= true; count:= count+1; p:= q; R:= R,p; P:= subsop(k=NULL,P); nP:= nP-1; break
%p fi
%p od;
%p if not found then break fi;
%p od:
%p R; # _Robert Israel_, Mar 04 2023
%t s = {2}; Do[p = 2; While[! FreeQ[s, p] || PrimeOmega[s[[-1]] + p] > 2, p = NextPrime[p]]; AppendTo[s, p], {200}]; s
%K nonn
%O 1,1
%A _Zak Seidov_, May 07 2022
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