

A233562


Products p*q of distinct primes such that (p*q + 1)/2 is a prime.


4



21, 33, 57, 85, 93, 133, 141, 145, 177, 201, 205, 213, 217, 253, 301, 381, 393, 445, 453, 481, 501, 537, 553, 565, 633, 697, 717, 745, 793, 817, 865, 913, 921, 933, 973, 1041, 1081, 1137, 1141, 1261, 1285, 1293, 1317, 1345, 1401, 1417, 1437, 1465, 1477, 1501
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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


LINKS

Table of n, a(n) for n=1..50.


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

Cf. A233561, A046388.
Cf. A128283.
Sequence in context: A271101 A191683 A032603 * A128283 A280878 A033901
Adjacent sequences: A233559 A233560 A233561 * A233563 A233564 A233565


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Dec 14 2013


STATUS

approved



