cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A195106 Numbers with largest and smallest prime factors differing by 4.

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%I A195106 #17 Feb 16 2025 08:33:15
%S A195106 21,63,77,105,147,189,221,315,437,441,525,539,567,735,847,945,1029,
%T A195106 1323,1517,1575,1701,2021,2205,2625,2835,2873,3087,3675,3757,3773,
%U A195106 3969,4725,4757,5103,5145,5929,6557,6615,7203,7875,8303,8505,9261,9317,9797,10051
%N A195106 Numbers with largest and smallest prime factors differing by 4.
%H A195106 Reinhard Zumkeller, <a href="/A195106/b195106.txt">Table of n, a(n) for n = 1..250</a>
%H A195106 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CousinPrimes.html">Cousin Primes</a>.
%F A195106 Sum_{n>=1} 1/a(n) = 1/48 + Sum_{n>=1} 1/A143203(n) = 1/48 + Sum_{n>=1} 1/((A023200(n)+1)^2-4) = 0.130715767205... . - _Amiram Eldar_, Oct 26 2024
%e A195106 a(10) = 441 = 3^2 * 7^2.
%e A195106 a(11) = 525 = 3 * 5^2 * 7.
%e A195106 a(12) = 539 = 7^2 * 11.
%t A195106 pf4Q[n_]:=Module[{pfs=Transpose[FactorInteger[n]][[1]]}, Max[pfs]- Min[pfs]==4]; Select[Range[11000],pf4Q] (* _Harvey P. Dale_, Sep 24 2011 *)
%o A195106 (Haskell)
%o A195106 a195106 n = a195106_list !! (n-1)
%o A195106 a195106_list = filter (\x -> a006530 x - a020639 x == 4) [1,3..]
%Y A195106 Cf. A023200, A143206, A195118.
%Y A195106 A143203 is a subsequence.
%K A195106 nonn
%O A195106 1,1
%A A195106 _Reinhard Zumkeller_, Sep 13 2011