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A100484 The primes doubled; Even semiprimes.

%I A100484 #124 Feb 16 2025 08:32:55
%S A100484 4,6,10,14,22,26,34,38,46,58,62,74,82,86,94,106,118,122,134,142,146,
%T A100484 158,166,178,194,202,206,214,218,226,254,262,274,278,298,302,314,326,
%U A100484 334,346,358,362,382,386,394,398,422,446,454,458,466,478,482,502,514,526
%N A100484 The primes doubled; Even semiprimes.
%C A100484 Essentially the same as A001747.
%C A100484 Right edge of the triangle in A065342. - _Reinhard Zumkeller_, Jan 30 2012
%C A100484 A253046(a(n)) > a(n). - _Reinhard Zumkeller_, Dec 26 2014
%C A100484 Apart from first term, these are the tau2-primes as defined in [Anderson, Frazier] and [Lanterman]. - _Michel Marcus_, May 15 2019
%C A100484 For every positive integer b and each m in this sequence b^(m-1) == b (mod m). - _Florian Baur_, Nov 26 2021
%H A100484 Charles R Greathouse IV, <a href="/A100484/b100484.txt">Table of n, a(n) for n = 1..10000</a>
%H A100484 D. D. Anderson and Andrea M. Frazier, <a href="https://doi.org/10.1216/RMJ-2011-41-3-663">On a general theory of factorization in integral domains</a>, Rocky Mountain J. Math., Volume 41, Number 3 (2011), 663-705. See pp. 698, 699, 702.
%H A100484 James Lanterman, <a href="https://arxiv.org/abs/1210.2991">Irreducibles in the Integers modulo n</a>, arXiv:1210.2991 [math.NT], 2012.
%H A100484 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Semiprime.html">Semiprime</a>
%F A100484 a(n) = 2 * A000040(n).
%F A100484 a(n) = A001747(n+1).
%F A100484 n>1: A000005(a(n)) = 4; A000203(a(n)) = 3*A008864(n); A000010(a(n)) = A006093(n); intersection of A001358 and A005843.
%F A100484 a(n) = A116366(n-1, n-1) for n>1. - _Reinhard Zumkeller_, Feb 06 2006
%F A100484 a(n) = A077017(n+1), n>1. - _R. J. Mathar_, Sep 02 2008
%F A100484 A078834(a(n)) = A000040(n). - _Reinhard Zumkeller_, Sep 19 2011
%F A100484 a(n) = A087112(n, 1). - _Reinhard Zumkeller_, Nov 25 2012
%F A100484 A000203(a(n)) = 3*n/2 + 3, n > 1. - _Wesley Ivan Hurt_, Sep 07 2013
%p A100484 A100484:=n->2*ithprime(n); seq(A100484(n), n=1..70); # _Wesley Ivan Hurt_, Mar 27 2014
%t A100484 2*Prime[Range[70]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 29 2008 *)
%o A100484 (PARI) 2*primes(70) \\ _Charles R Greathouse IV_, Aug 21 2011
%o A100484 (Haskell)
%o A100484 a100484 n = a100484_list !! (n-1)
%o A100484 a100484_list = map (* 2) a000040_list
%o A100484 -- _Reinhard Zumkeller_, Jan 31 2012
%o A100484 (Magma) [2*p: p in PrimesUpTo(350)]; // _Vincenzo Librandi_, Mar 27 2014
%o A100484 (GAP) 2*Filtered([1..300],IsPrime); # _Muniru A Asiru_, Oct 05 2018
%o A100484 (GAP) List([1..70], n-> 2*Primes[n]); # _G. C. Greubel_, May 18 2019
%o A100484 (Sage) [2*nth_prime(n) for n in (1..70)] # _G. C. Greubel_, May 18 2019
%Y A100484 Subsequence of A091376. After the initial 4 also a subsequence of A039956.
%Y A100484 Cf. A046315, A152099, A179740.
%Y A100484 Cf. A001748, A253046, A353478 (characteristic function).
%Y A100484 Row 3 of A286625, column 3 of A286623.
%K A100484 nonn,easy
%O A100484 1,1
%A A100484 _Reinhard Zumkeller_, Nov 22 2004
%E A100484 Simpler definition.