A100484 The primes doubled; Even semiprimes.

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

Author

Reinhard Zumkeller, Nov 22 2004

Keywords

• nonn
• easy

Comments

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

Crossrefs

Subsequence of A091376. After the initial 4 also a subsequence of A039956.

Cf. A046315, A152099, A179740.

Cf. A001748, A253046, A353478 (characteristic function).

Row 3 of A286625, column 3 of A286623.

Programs

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

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

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 *)

PARI

2*primes(70) \\ Charles R Greathouse IV, Aug 21 2011

Sage

[2*nth_prime(n) for n in (1..70)] # G. C. Greubel, May 18 2019

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

Extensions

Simpler definition.