A100484 The primes doubled.

4, 6, 10, 14, 22, 26, 34, 38, 46, 58, 62, 74, 82, 86, 94, 106, 118, 122, 134, 142, 146, 158, 166, 178, 194, 202, 206, 214, 218, 226, 254, 262, 274, 278, 298, 302, 314, 326, 334, 346, 358, 362, 382, 386, 394, 398, 422, 446, 454, 458, 466, 478, 482, 502, 514, 526

Offset

1,1

Comments

Even semiprimes.

Essentially the same as A001747.

Right edge of the triangle in A065342. - Reinhard Zumkeller, Jan 30 2012

A253046(a(n)) > a(n). - Reinhard Zumkeller, Dec 26 2014

Apart from first term, these are the tau2-primes as defined in [Anderson, Frazier] and [Lanterman]. - Michel Marcus, May 15 2019

For every positive integer b and each m in this sequence b^(m-1) == b (mod m). - Florian Baur, Nov 26 2021

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

D. D. Anderson and Andrea M. Frazier, On a general theory of factorization in integral domains, Rocky Mountain J. Math., Volume 41, Number 3 (2011), 663-705. See pp. 698, 699, 702.

James Lanterman, Irreducibles in the Integers modulo n, arXiv:1210.2991 [math.NT], 2012.

Eric Weisstein's World of Mathematics, Semiprime

Formula

a(n) = 2 * A000040(n).

a(n) = A001747(n+1).

n>1: A000005(a(n)) = 4; A000203(a(n)) = 3*A008864(n); A000010(a(n)) = A006093(n); intersection of A001358 and A005843.

a(n) = A116366(n-1, n-1) for n>1. - Reinhard Zumkeller, Feb 06 2006

a(n) = A077017(n+1), n>1. - R. J. Mathar, Sep 02 2008

A078834(a(n)) = A000040(n). - Reinhard Zumkeller, Sep 19 2011

a(n) = A087112(n, 1). - Reinhard Zumkeller, Nov 25 2012

A000203(a(n)) = 3*n/2 + 3, n > 1. - Wesley Ivan Hurt, Sep 07 2013

Maple

A100484:=n->2*ithprime(n); seq(A100484(n), n=1..70); # Wesley Ivan Hurt, Mar 27 2014

Mathematica

2*Prime[Range[70]] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)

Prog

(PARI) 2*primes(70) \\ Charles R Greathouse IV, Aug 21 2011
(Haskell)
a100484 n = a100484_list !! (n-1)
a100484_list = map (* 2) a000040_list
-- Reinhard Zumkeller, Jan 31 2012
(Magma) [2*p: p in PrimesUpTo(350)]; // Vincenzo Librandi, Mar 27 2014
(GAP) 2*Filtered([1..300], IsPrime); # Muniru A Asiru, Oct 05 2018
(GAP) List([1..70], n-> 2*Primes[n]); # G. C. Greubel, May 18 2019
(Sage) [2*nth_prime(n) for n in (1..70)] # G. C. Greubel, May 18 2019

Crossrefs

Subsequence of A091376.

Cf. A046315, A152099, A179740.

Cf. A001748, A253046.

Row 3 of A286625, column 3 of A286623.

Sequence in context: A243428 A091376 A363134 * A076924 A103801 A141247

Adjacent sequences: A100481 A100482 A100483 * A100485 A100486 A100487

Keyword

nonn,easy,changed

Author

Reinhard Zumkeller, Nov 22 2004

Extensions

Simpler definition.

Status

approved