A108172 Semiprimes p*q where p is a prime of the form 6n+1 (A002476) and q is a prime of the form 6n-1 (A007528).

35, 65, 77, 95, 119, 143, 155, 161, 185, 203, 209, 215, 221, 287, 299, 305, 323, 329, 335, 341, 365, 371, 377, 395, 407, 413, 437, 473, 485, 497, 515, 527, 533, 545, 551, 581, 611, 623, 629, 635, 671, 689, 695, 707, 713, 731, 737, 749, 755, 767, 779, 785

Offset: 1

Author

Jonathan Vos Post, Jun 13 2005

Keywords

• easy
• nonn

Comments

Also semiprimes of the form 6n-1 (or 6n+5).

Every semiprime not divisible by 2 or 3 must be in one of these three disjoint sets:

A108164 - the product of two primes of the form 6n+1 (A002476),

A108166 - the product of two primes of the form 6n-1 (A007528),

A108172 - the product of a prime of the form 6n+1 and a prime of the form 6n-1.

The product of a prime of the form 6n+1 and a prime of the form 6n-1 is a semiprime of the form 6n-1.

There are 740 of these numbers below 10,000.

References

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 870.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Crossrefs

Cf. A001358, A002476, A007528, A190299.

Programs

Mathematica

Select[Range[15,1000,2], Last/@FactorInteger[#]=={1,1} && IntegerQ[(#-2)/3]&] (* Vladimir Joseph Stephan Orlovsky, May 07 2011 *)

PARI

list(lim)=my(v=List(),t); forprime(p=5, lim\7, if(p%6<5, next); forprime(q=7, lim\5, if(q%6>1, next); t=p*q; if(t>lim, break); listput(v, t))); Set(v) \\ Charles R Greathouse IV, Feb 08 2017

Formula

a(n) = 6 * A112776(n) + 5.

Extensions

Edited by Ray Chandler, Oct 15 2005