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

1,1

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].

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A001358, A002476, A007528, A190299.

Sequence in context: A350344 A245274 A092256 * A354502 A176875 A292005

Adjacent sequences: A108169 A108170 A108171 * A108173 A108174 A108175

Keyword

easy,nonn

Author

Jonathan Vos Post, Jun 13 2005

Extensions

Edited by Ray Chandler, Oct 15 2005

Status

approved