A177213 Numbers k that are the products of two distinct primes such that 2*k-1, 4*k-3, 8*k-7 and 16*k-15 are also products of two distinct primes.

247, 295, 478, 634, 694, 721, 1255, 1267, 1294, 1387, 1546, 1762, 1942, 2323, 2374, 2773, 3005, 3334, 3403, 3883, 3949, 4126, 4714, 4741, 4777, 5062, 5269, 5287, 5353, 5422, 5617, 6583, 6805, 7273, 7495, 8587, 8767, 9017, 9406, 9427, 9847, 10018

Offset

1,1

Links

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

Example

247 is a term because 247 = 13*19, 2*247 - 1 = 493 = 17*29, 4*247 - 3 = 985 = 5*197, 8*247 - 1 = 1969 = 11*179, and 16*247 - 15 = 3937 = 31*127.

Mathematica

f[n_]:=Last/@FactorInteger[n]=={1, 1}; lst={}; Do[If[f[n]&&f[2*n-1]&&f[4*n-3]&&f[8*n-7]&&f[16*n-15], AppendTo[lst, n]], {n, 0, 8!}]; lst
ptdpQ[n_]:=PrimeNu[n]==PrimeOmega[n]==2; Select[Range[11000], AllTrue[ {#, 2#-1, 4#-3, 8#-7, 16#-15}, ptdpQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 30 2016 *)

Crossrefs

Cf. A006881, A177210, A177211, A177212.

Sequence in context: A351243 A175043 A051977 * A283737 A020313 A318055

Adjacent sequences: A177210 A177211 A177212 * A177214 A177215 A177216

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 04 2010

Status

approved