OFFSET
1,1
COMMENTS
Starting with a(3) = 3, (a(n) + a(n-1))/2 is a prime.
For n >= 4, a(n) == 11 (mod 12). Conjecture: every prime == 11 (mod 12) occurs in the sequence. - Robert Israel, Mar 04 2023
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
2+7=9=3*3, 7+3=10=2*5, 3+11=14=2*7 are all semiprimes.
MAPLE
R:= 2, 7: p:= 7: P:= select(isprime, [3, seq(i, i=11..2000, 12)]):
nP:= nops(P): count:= 2:
do
found:= false;
for k from 1 to nops(P) do
q:= P[k];
if isprime((p+q)/2) then
found:= true; count:= count+1; p:= q; R:= R, p; P:= subsop(k=NULL, P); nP:= nP-1; break
fi
od;
if not found then break fi;
od:
R; # Robert Israel, Mar 04 2023
MATHEMATICA
s = {2}; Do[p = 2; While[! FreeQ[s, p] || PrimeOmega[s[[-1]] + p] > 2, p = NextPrime[p]]; AppendTo[s, p], {200}]; s
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, May 07 2022
STATUS
approved