A346180 a(n) = prime(n) + n if n is prime, a(n) = prime(n) otherwise.

2, 5, 8, 7, 16, 13, 24, 19, 23, 29, 42, 37, 54, 43, 47, 53, 76, 61, 86, 71, 73, 79, 106, 89, 97, 101, 103, 107, 138, 113, 158, 131, 137, 139, 149, 151, 194, 163, 167, 173, 220, 181, 234, 193, 197, 199, 258, 223, 227, 229, 233, 239, 294, 251, 257, 263, 269, 271

Offset

1,1

Comments

For n > 0, take the n-th prime and only add n to it if n is prime itself.

Links

Table of n, a(n) for n=1..58.

Formula

a(n) = A000040(n) + A061397(n).

Example

a(1) = 2 = 2+0; 2 is the first prime. 1 is not prime and thus is not added.
a(2) = 5 = 3+2; 3 is the second prime, and since 2 is also prime, add 2.
a(3) = 8 = 5+3; 5 is the third prime, and since 3 is also prime, add 3.

Mathematica

Table[Prime@n+Boole@PrimeQ[n]n, {n, 60}] (* Giorgos Kalogeropoulos, Jul 29 2021 *)
Table[If[PrimeQ[n], Prime[n]+n, Prime[n]], {n, 60}] (* Harvey P. Dale, Nov 20 2022 *)

Prog

(PARI) a(n) = prime(n) + isprime(n)*n; \\ Michel Marcus, Jul 12 2021
(Python)
from sympy import isprime, prime
def a(n): return prime(n) + n*isprime(n)
print([a(n) for n in range(1, 59)]) # Michael S. Branicky, Jul 29 2021
(Python) # faster version for initial segment of sequence
from sympy import isprime, prime, primerange
def aupton(nn): return [p + n*isprime(n) for n, p in enumerate(primerange(1, prime(nn)+1), start=1)]
print(aupton(10000)) # Michael S. Branicky, Jul 29 2021

Crossrefs

Cf. A000040, A061397.

Sequence in context: A250206 A138371 A140053 * A103311 A019824 A284868

Adjacent sequences: A346177 A346178 A346179 * A346181 A346182 A346183

Keyword

nonn

Author

Samuel Vilz, Jul 09 2021

Status

approved