login
A177211
Numbers k that are the products of two distinct primes such that 2*k-1 and 4*k-3 are also products of two distinct primes.
11
33, 118, 119, 134, 146, 226, 247, 249, 287, 295, 334, 335, 386, 391, 393, 395, 422, 478, 493, 497, 502, 519, 551, 583, 589, 614, 629, 634, 694, 697, 721, 731, 749, 755, 789, 802, 817, 843, 879, 898, 955, 958, 985, 989, 1003, 1037, 1079, 1114, 1154, 1159, 1177
OFFSET
1,1
LINKS
EXAMPLE
33 is a term because 33 = 3*11, 2*33 - 1 = 65 = 5*13 and 2*65 - 1 = 4*33 - 3 = 129 = 3*43.
MATHEMATICA
f[n_]:=Last/@FactorInteger[n]=={1, 1}; lst={}; Do[If[f[n]&&f[2*n-1]&&f[4*n-3], AppendTo[lst, n]], {n, 0, 7!}]; lst
tdpQ[n_]:=PrimeNu[n]==PrimeOmega[n]==PrimeNu[2n-1]==PrimeOmega[2n-1] == PrimeNu[4n-3]==PrimeOmega[4n-3]==2; Select[Range[1200], tdpQ] (* Harvey P. Dale, Nov 15 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Definition clarified by Harvey P. Dale, Nov 15 2020
STATUS
approved