A037168 a(n) = 2*prime(n) - 2.

2, 4, 8, 12, 20, 24, 32, 36, 44, 56, 60, 72, 80, 84, 92, 104, 116, 120, 132, 140, 144, 156, 164, 176, 192, 200, 204, 212, 216, 224, 252, 260, 272, 276, 296, 300, 312, 324, 332, 344, 356, 360, 380, 384, 392, 396, 420, 444, 452, 456

Offset: 1

Author

Armand Turpel (armandt(AT)unforgettable.com)

Keywords

• nonn
• easy

Comments

Original definition: Prime(n)+ Sum(prime(n-z) mod prime(n-z-1)); z=0,1...n-2 ; with offset 2.

Since prime(n+1) < 2*prime(n) for all n, the "mod" in the sum is equivalent to "-", making it telescopic and equal to prime(n)-2. - M. F. Hasler, Jun 29 2013

Examples

			a(3) = 8 since the third prime is 5 and 2 * 5 - 2 = 8.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Barry Brent, On the constant terms of certain meromorphic modular forms for Hecke groups, arXiv:2212.12515 [math.NT], 2022.
• Barry Brent, On the Constant Terms of Certain Laurent Series, Preprints (2023) 2023061164.

Crossrefs

Cf. A000010, A000040, A006093, A023900.

Programs

Magma

[2*p-2: p in PrimesUpTo(300)]; // Vincenzo Librandi, Mar 19 2014

Mathematica

2Prime[Range[50]] - 2 (* Alonso del Arte, Jun 30 2013 *)

PARI

A037168 = n->prime(n)*2-2  \\ M. F. Hasler, Jun 29 2013

Formula

a(n) = 2 * prime(n) - 2 = 2 * phi(prime(n)). - Alonso del Arte, Jun 30 2013

a(n) = 2 * A006093(n). - Ray Chandler, Jun 30 2013

a(n) = A000010(A000040(n)) - A023900(A000040(n)). - Torlach Rush, Mar 11 2018

Extensions

Definition simplified and extended to n=1, following a suggestion from Alonso del Arte, by M. F. Hasler, Jun 29 2013