A179740 -id:A179740 - cp's OEIS frontend

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

Reinhard Zumkeller, Nov 22 2004

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

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

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.

2*Filtered([1..300],IsPrime); # Muniru A Asiru, Oct 05 2018

List([1..70], n-> 2*Primes[n]); # G. C. Greubel, May 18 2019

a100484 n = a100484_list !! (n-1)
a100484_list = map (* 2) a000040_list
-- Reinhard Zumkeller, Jan 31 2012

[2*p: p in PrimesUpTo(350)]; // Vincenzo Librandi, Mar 27 2014

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

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

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

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

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

Simpler definition.

A031215 Even-indexed primes: a(n) = prime(2n).

Original entry on oeis.org

3, 7, 13, 19, 29, 37, 43, 53, 61, 71, 79, 89, 101, 107, 113, 131, 139, 151, 163, 173, 181, 193, 199, 223, 229, 239, 251, 263, 271, 281, 293, 311, 317, 337, 349, 359, 373, 383, 397, 409, 421, 433, 443, 457, 463, 479, 491, 503, 521, 541, 557, 569

Offset: 1

Jeff Burch

Also every second odd prime. - Cino Hilliard, Dec 02 2007

If n > 1, then a(n) is less than, and asymptotic to, the n-th Ramanujan prime R_n = A104272(n). Research questions on the difference R_n - a(n) are at A104272. - Jonathan Sondow, Dec 16 2013

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Cf. A000040, A031368 (odd-indexed primes), A104272, A105720, A161463, A179740, A233739.

[ NthPrime(2*n): n in [1..1000] ]; // Vincenzo Librandi, Apr 11 2011

Maple
```
A031215 := n->ithprime(2*n);
```

Table[ Prime[ 2n], {n, 52}] (* Robert G. Wilson v, Dec 01 2013 *)

a(n)=prime(2*n) \\ Charles R Greathouse IV, Jul 02 2013

a(n) = A104272(n) - A233739(n). - Jonathan Sondow, Dec 16 2013

a(n) = A105720(n) - A161463(n). - Torlach Rush, May 31 2021

A066066 a(n) = prime(2n) - 2prime(n).

Original entry on oeis.org

-1, 1, 3, 5, 7, 11, 9, 15, 15, 13, 17, 15, 19, 21, 19, 25, 21, 29, 29, 31, 35, 35, 33, 45, 35, 37, 45, 49, 53, 55, 39, 49, 43, 59, 51, 57, 59, 57, 63, 63, 63, 71, 61, 71, 69, 81, 69, 57, 67, 83, 91, 91, 95, 91, 87, 87, 81, 99, 93, 97, 107, 97, 87, 97, 107, 109, 95, 95, 93, 111, 115, 109, 105, 111, 105, 115, 109, 117, 127, 123, 115

Offset: 1

Reinhard Zumkeller, Dec 01 2001

sign

a(n) = A022457(n) for n > 1.
a(n) = A031215(n)-A100484(n) = A072473(n)-A000040(n); see A179740 for primes. - Reinhard Zumkeller, Jul 25 2010
Asymptotically, a(n) ~ log(4) n, with log(4) = 2 log 2 = 1.38629436111989... = A016627. - M. F. Hasler, Oct 19 2013

Harry J. Smith, Table of n, a(n) for n = 1..1000

Table[Prime[2n]-2Prime[n],{n,100}] (* Harvey P. Dale, Aug 21 2016 *)

{ for (n = 1, 1000, a=prime(2*n) - prime(n)*2; write("b066066.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 09 2009

A066066(n)=prime(2*n)-2*prime(n) \\ M. F. Hasler, Oct 19 2013

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A100484 The primes doubled; Even semiprimes.

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A031215 Even-indexed primes: a(n) = prime(2n).

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A066066 a(n) = prime(2*n) - 2*prime(n).

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A066066 a(n) = prime(2n) - 2prime(n).