A177212 Numbers k that are the products of two distinct primes such that 2*k-1, 4*k-3 and 8*k-7 are also products of two distinct primes.

247, 249, 295, 395, 422, 478, 493, 502, 519, 589, 634, 694, 721, 755, 955, 1255, 1267, 1294, 1306, 1351, 1387, 1441, 1522, 1546, 1727, 1762, 1942, 2031, 2119, 2155, 2323, 2374, 2449, 2491, 2509, 2533, 2587, 2623, 2661, 2733, 2773, 3005, 3039, 3091, 3334

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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

Maple

isA006881:= proc(n) local F;
  F:= ifactors(n)[2];
  nops(F)=2 and F[1, 2]+F[2, 2]=2
end proc:
filter:= n -> andmap(isA006881, [n, 2*n-1, 4*n-3, 8*n-7]);
select(filter, [$1..10000]); # Robert Israel, Jul 11 2017

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], AppendTo[lst, n]], {n, 0, 3*7!}]; lst
p2dpQ[n_]:=Transpose[FactorInteger[n]][[2]]=={1, 1}; With[{s=Select[Range[ 3500], p2dpQ]}, Select[s, AllTrue[{2#-1, 4#-3, 8#-7}, p2dpQ]&]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 27 2015 *)

Crossrefs

Cf. A006881, A177210, A177211.

Sequence in context: A289334 A251516 A208188 * A044983 A351243 A175043

Adjacent sequences: A177209 A177210 A177211 * A177213 A177214 A177215

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 04 2010

Status

approved