OFFSET
1,1
COMMENTS
This sequence is a subsequence of A128283 since the condition that (p+q)/2 be prime is not required here. The smallest number not in A128283 is 141=3*47 since (3+47)/2=25. - Hartmut F. W. Hoft, Oct 31 2020
EXAMPLE
21 = 3*7 is the least product of distinct primes p and q for which (p*q + 1)/2 is a prime, so a(1) = 21.
MATHEMATICA
t = Select[Range[1, 7000, 2], Map[Last, FactorInteger[#]] == Table[1, {2}] &]; Take[(t + 1)/2, 120] (* A234096 *)
v = Flatten[Position[PrimeQ[(t + 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}] (* A233562 *)
(w + 1)/2 (* A234098 *) (* Peter J. C. Moses, Dec 23 2013 *)
With[{nn=50}, Take[Union[Select[Times@@@Subsets[Prime[Range[2nn]], {2}], PrimeQ[ (#+1)/2]&]], nn]] (* Harvey P. Dale, Mar 24 2015 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Dec 14 2013
STATUS
approved