A233561 Products p*q of distinct primes such that (p*q - 1)/2 is prime.

15, 35, 39, 87, 95, 119, 123, 143, 159, 203, 215, 219, 299, 303, 327, 335, 395, 447, 515, 527, 543, 623, 635, 695, 699, 707, 767, 779, 803, 843, 879, 899, 923, 959, 1007, 1043, 1047, 1115, 1139, 1199, 1203, 1227, 1263, 1347, 1355, 1383, 1403, 1623, 1643

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

15 = 3*5 is the least product of distinct primes p and q for which (p*q - 1)/2 is prime, so a(1) = 15.

Mathematica

t = Select[Range[1, 7000, 2], Map[Last, FactorInteger[#]] == Table[1, {2}] &]; Take[(t - 1)/2, 120] (* A234093 *)
v = Flatten[Position[PrimeQ[(t - 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}]  (* A233561 *)
(w - 1)/2 (* A234095 *)  (* Peter J. C. Moses, Dec 23 2013 *)
With[{upto=2000}, Select[Times@@#&/@Select[Subsets[Prime[Range[ PrimePi[ upto/2]]], {2}], PrimeQ[(Times@@#-1)/2]&]//Union, #<=upto&]] (* Harvey P. Dale, Nov 02 2017 *)

Crossrefs

Cf. A234093, A234095, A046388.

Sequence in context: A080774 A146319 A238605 * A114988 A130871 A332378

Adjacent sequences: A233558 A233559 A233560 * A233562 A233563 A233564

Keyword

nonn,easy

Author

Clark Kimberling, Dec 14 2013

Status

approved