A345727 a(n) = (prime(n)+1) * prime(n+1).

9, 20, 42, 88, 156, 238, 342, 460, 696, 930, 1184, 1558, 1806, 2068, 2544, 3186, 3660, 4154, 4828, 5256, 5846, 6640, 7476, 8730, 9898, 10506, 11128, 11772, 12430, 14478, 16768, 18084, 19182, 20860, 22650, 23864, 25754, 27388, 29064, 31146, 32580, 34762

Offset: 1

Author

Simon Strandgaard, Jul 20 2021

Keywords

• nonn

Examples

			a(1) = (prime(1)+1) * prime(2) = 3 *  3 =  9,
a(2) = (prime(2)+1) * prime(3) = 4 *  5 = 20,
a(3) = (prime(3)+1) * prime(4) = 6 *  7 = 42,
a(4) = (prime(4)+1) * prime(5) = 8 * 11 = 88.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A006094, A008864, A123134, A180617.

Programs

Maple

A345727 := proc(n)
    (ithprime(n)+1)*ithprime(n+1) ;
end proc:
seq(A345727(n),n=1..10) ; # R. J. Mathar, Aug 16 2021

Mathematica

(Prime@#+1)Prime[#+1]&/@Range@50 (* Giorgos Kalogeropoulos, Jul 23 2021 *)
(#[[1]]+1)#[[2]]&/@Partition[Prime[Range[50]],2,1] (* Harvey P. Dale, Jan 08 2023 *)

PARI

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

Ruby

require 'prime'
values = []
primes = Prime.first(20)
primes.each_index do |n|
    next if n < 1
    values << (primes[n - 1] + 1) * primes[n]
end
p values

Formula

a(n) = A008864(n)*A000040(n+1).

a(n) = A180617(n)-A008864(n).

a(n) = A006094(n)+A000040(n+1).