

A108172


Semiprimes p*q where p is a prime of the form 6n+1 (A002476) and q is a prime of the form 6n1 (A007528).


4



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
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OFFSET

1,1


COMMENTS

Also semiprimes of the form 6n1 (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 6n1 (A007528),
A108172  the product of a prime of the form 6n+1 and a prime of the form 6n1.
The product of a prime of the form 6n+1 and a prime of the form 6n1 is a semiprime of the form 6n1.
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: A250764 A245274 A092256 * A176875 A292005 A331378
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



