A180617 -id:A180617 - cp's OEIS frontend

A126199 a(n) = prime(n)*prime(n+1) + prime(n) + prime(n+1).

11, 23, 47, 95, 167, 251, 359, 479, 719, 959, 1215, 1595, 1847, 2111, 2591, 3239, 3719, 4215, 4895, 5327, 5919, 6719, 7559, 8819, 9995, 10607, 11231, 11879, 12539, 14591, 16895, 18215, 19319, 20999, 22799, 24015, 25911, 27551, 29231, 31319, 32759

Offset: 1

Jonathan Vos Post, Mar 08 2007

Cf. A000040, A001043, A006094, A126148, A096342, A180617.

f[n_] := Block[{p = Prime[n], q = Prime[n + 1]}, p*q + p + q]; Array[f, 42] (* Robert G. Wilson v, Mar 09 2007 *)
Times@@#+Total[#]&/@Partition[Prime[Range[50]],2,1] (* Harvey P. Dale, Nov 01 2017 *)

a(n) = A180617(n) - 1. - Omar E. Pol, Dec 08 2019

More terms from Robert G. Wilson v, Mar 09 2007

A309772 Least common multiple of prime(n+1)+1 and prime(n)+1.

Original entry on oeis.org

12, 12, 24, 24, 84, 126, 180, 120, 120, 480, 608, 798, 924, 528, 432, 540, 1860, 2108, 1224, 2664, 2960, 1680, 1260, 4410, 4998, 5304, 2808, 5940, 6270, 7296, 4224, 3036, 9660, 2100, 11400, 12008, 12956, 6888, 4872, 5220, 16380, 17472, 18624, 19206, 19800, 10600

Offset: 1

Daniel Hoyt, Aug 16 2019

a(n) = (prime(n)+1)*(prime(n+1)+1)/2 if n is in A066940. - Robert Israel, Aug 16 2019

Daniel Hoyt, Table of n, a(n) for n = 1..1000

Cf. A008864, A063086 (gcd), A066940, A180617 (product).

[Lcm(1+NthPrime(n),1+NthPrime(n+1)):n in [1..50]]; // Marius A. Burtea, Aug 16 2019

P:= [seq(ithprime(i),i=1..100)]:
seq(ilcm(P[i]+1,P[i+1]+1),i=1..99); # Robert Israel, Aug 16 2019

Array[LCM[Prime[#] + 1, Prime[# + 1] + 1] &, 50] (* Amiram Eldar, Aug 16 2019 *)

a(n) = lcm(A008864(n+1), A008864(n)) = lcm(prime(n+1)+1, prime(n)+1).

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

Original entry on oeis.org

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

Simon Strandgaard, Jul 20 2021

nonn

			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.

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

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

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

(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 *)

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

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

a(n) = A008864(n)*A000040(n+1).
a(n) = A180617(n)-A008864(n).
a(n) = A006094(n)+A000040(n+1).

cp's OEIS Frontend

A126199 a(n) = prime(n)*prime(n+1) + prime(n) + prime(n+1).

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A309772 Least common multiple of prime(n+1)+1 and prime(n)+1.

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

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