login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A143203 Numbers having exactly two distinct prime factors p, q with q=p+4. 5

%I #14 Mar 18 2023 09:52:33

%S 21,63,77,147,189,221,437,441,539,567,847,1029,1323,1517,1701,2021,

%T 2873,3087,3757,3773,3969,4757,5103,5929,6557,7203,8303,9261,9317,

%U 9797,10051,11021,11907,12317,15309,16637,21609

%N Numbers having exactly two distinct prime factors p, q with q=p+4.

%C A143201(a(n)) = 5;

%C A020639(a(n))in A023200 and A006530(a(n)) in A046132;

%C subsequence of A007774: A001221(a(n))=2.

%C A033850 is a subsequence; subsequence of A195106. [_Reinhard Zumkeller_, Sep 13 2011]

%H Reinhard Zumkeller, <a href="/A143203/b143203.txt">Table of n, a(n) for n = 1..250</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CousinPrimes.html">Cousin Primes</a>

%H <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>

%e a(1) = 21 = 3 * 7 = A023200(1) * A046132(1);

%e a(2) = 63 = 3^2 * 7 = A023200(1)^2 * A046132(1);

%e a(3) = 77 = 7 * 11 = A023200(2) * A046132(2);

%e a(4) = 147 = 3 * 7^2 = A023200(1) * A046132(1)^2;

%e a(5) = 189 = 3*3 * 7 = A023200(1)^3 * A046132(1);

%e a(6) = 221 = 13 * 17 = A023200(3) * A046132(3);

%e a(7) = 437 = 19 * 23 = A023200(4) * A046132(4);

%e a(8) = 441 = 3^2 * 7^2 = A023200(1)^2 * A046132(1)^2;

%e a(9) = 539 = 7^2 * 11 = A023200(2)^2 * A046132(2);

%e a(10) = 567 = 3^4 * 7 = A023200(1)^4 * A046132(1).

%t dpf2Q[n_]:=Module[{fi=FactorInteger[n][[;;,1]]},Length[fi]==2&&fi[[2]]-fi[[1]]==4]; Select[Range[22000],dpf2Q] (* _Harvey P. Dale_, Mar 18 2023 *)

%o (Haskell)

%o a143203 n = a143203_list !! (n-1)

%o a143203_list = filter f [1,3..] where

%o f x = length pfs == 2 && last pfs - head pfs == 4 where

%o pfs = a027748_row x

%o -- _Reinhard Zumkeller_, Sep 13 2011

%Y Cf. A027748, A001221, A020639, A006530.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Aug 12 2008

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)