A157352 Products (semiprimes) of two distinct safe primes.

35, 55, 77, 115, 161, 235, 253, 295, 329, 413, 415, 517, 535, 581, 649, 749, 835, 895, 913, 1081, 1135, 1169, 1177, 1253, 1315, 1357, 1589, 1735, 1795, 1837, 1841, 1909, 1915, 1969, 2335, 2395, 2429, 2461, 2497, 2513, 2515, 2681, 2773, 2815, 2893, 2935

Offset

1,1

Comments

35=5*7; 5 and 7 are safe primes, 55=5*11; 5 and 11 are safe primes,...

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

a(1) = 35 since 35 = 5 * 7, and (5 - 1)/2 = 2 and (7 - 1)/2 = 3 are both prime, thus 5 and 7 are distinct safe primes.

Mathematica

lst={}; Do[If[Plus@@Last/@FactorInteger[n]==2, a=Length[First/@FactorInteger[n]]; If[a==2, b=First/@FactorInteger[n]; c=b[[1]]; d=b[[2]]; If[PrimeQ[(c-1)/2]&&PrimeQ[(d-1)/2], AppendTo[lst, n]]]], {n, 7!}]; lst
Select[Select[Range@ 3000, PrimeNu@ # == 2 &], Times @@ Map[If[PrimeQ[(# - 1)/2], #, 0] &, Map[First, FactorInteger@ #]] == # &] (* Michael De Vlieger, Feb 28 2016 *)
Module[{upto=3000, sp}, sp=Select[Prime[Range[PrimePi[upto/5]]], PrimeQ[(#-1)/2]&]; Select[Union[Times@@@Subsets[sp, {2}]], #<+upto&]] (* Harvey P. Dale, Aug 25 2017 *)

Crossrefs

Cf. A001358, A005384, A005385, A006881, A007304, A111206, A157342, A157344, A157345, A157346, A157347.

Sequence in context: A121707 A267999 A319386 * A176255 A355814 A090877

Adjacent sequences: A157349 A157350 A157351 * A157353 A157354 A157355

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Feb 27 2009

Extensions

Example corrected by Harvey P. Dale, Aug 25 2017

Status

approved