A123134 a(n) = prime(n)*(prime(n+1) + 1).

8, 18, 40, 84, 154, 234, 340, 456, 690, 928, 1178, 1554, 1804, 2064, 2538, 3180, 3658, 4148, 4824, 5254, 5840, 6636, 7470, 8722, 9894, 10504, 11124, 11770, 12426, 14464, 16764, 18078, 19180, 20850, 22648, 23858, 25748, 27384, 29058, 31140, 32578

Offset: 1

Author

Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 30 2006

Keywords

• nonn

Comments

All terms are even. - Michel Marcus, Apr 02 2017

Examples

			a(1) = 2*(3+1) = 8, a(2) = 3*(5+1) = 18, a(3) = 5*(7+1) = 40, ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• A. Frank & P. Jacqueroux, International Contest, 2001. Item 21

Crossrefs

Cf. A000040, A008864, A286624.

Programs

Magma

[NthPrime(n)*(NthPrime(n+1) +1): n in [1..40]]; // G. C. Greubel, Aug 04 2021

Mathematica

a[n_]:=Prime[n](Prime[n+1]+1); Array[a, 80] (* Giovanni Resta, Apr 02 2017 *)
#[[1]](#[[2]]+1)&/@Partition[Prime[Range[50]],2,1] (* Harvey P. Dale, Jan 06 2019 *)

PARI

for(n=1,100,print1(prime(n)*(prime(n+1)+1),","))

Python

from sympy import prime
def a(n): return prime(n) * (prime(n + 1) + 1) # Indranil Ghosh, Apr 02 2017

Formula

a(n) = A000040(n)*A008864(n+1). - Zak Seidov, Apr 02 2017

a(n) = A286624(n) - 1. - Antti Karttunen, Jul 06 2017