A177223 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.

145, 203, 291, 298, 407, 497, 649, 707, 758, 815, 899, 926, 959, 995, 1079, 1094, 1139, 1142, 1157, 1313, 1403, 1415, 1461, 1497, 1538, 1639, 1658, 1691, 1857, 1934, 1945, 1991, 2123, 2159, 2217, 2234, 2315, 2603, 2629, 2807, 2991, 3215, 3254, 3279, 3305

Offset

1,1

Comments

A number k is the product of two distinct primes iff k = p*q where p and q are distinct primes. - N. J. A. Sloane, Jan 11 2025

Links

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

Example

145 is a term because 145 = 5*29, 2*145 + 1 = 291 = 3*97, 4*145 + 1 = 583 = 11*53, and 8*145 + 1 = 1167 = 3*389.

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, 2*7!}]; lst
tdpQ[n_]:=With[{c={n, 2n+1, 4n+3, 8n+7}}, PrimeNu[c]==PrimeOmega[c]=={2, 2, 2, 2}]; Select[Range[3500], tdpQ] (* Harvey P. Dale, Jan 11 2025 *)

Crossrefs

Cf. A006881, A111153, A177210, A177211, A177212, A177213, A177214, A177215, A177216, A177217, A177220, A177221, A177222.

Sequence in context: A326258 A051414 A176699 * A318530 A158133 A094613

Adjacent sequences: A177220 A177221 A177222 * A177224 A177225 A177226

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 05 2010

Status

approved