A014683 In the sequence of positive integers add 1 to each prime number.

1, 3, 4, 4, 6, 6, 8, 8, 9, 10, 12, 12, 14, 14, 15, 16, 18, 18, 20, 20, 21, 22, 24, 24, 25, 26, 27, 28, 30, 30, 32, 32, 33, 34, 35, 36, 38, 38, 39, 40, 42, 42, 44, 44, 45, 46, 48, 48, 49, 50, 51, 52, 54, 54, 55, 56, 57, 58, 60, 60, 62, 62, 63, 64, 65, 66, 68, 68, 69, 70, 72, 72

Offset

1,2

Comments

For n >= 3, a(n) = smallest composite number m such that m - (n-2) is a prime. - Amarnath Murthy and Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Mar 08 2003

Möbius transform of sigma(n)+omega(n) = A380457(n). - Wesley Ivan Hurt, Jun 22 2025

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..10000

Formula

a(n) = n + pi(n) - pi(n-1). - Wesley Ivan Hurt, Jun 15 2013

a(n) = n + A010051(n). - Reinhard Zumkeller, Nov 01 2014

a(n) = Sum_{d|n} A380457(d)*mu(n/d). - Wesley Ivan Hurt, Jun 22 2025

Mathematica

Array[If[PrimeQ[#], #+1, #]&, 80] (* Harvey P. Dale, Jul 21 2013 *)

Prog

(PARI) a(n)=n+isprime(n)
(Haskell)
a014683 n = n + a010051' n  -- Reinhard Zumkeller, Nov 01 2014
(Python)
from sympy import isprime
def A014683(n): return n+isprime(n) # Chai Wah Wu, Oct 03 2024

Crossrefs

Cf. A010051, A113646, A380457.

Sequence in context: A215250 A354154 A229022 * A213222 A166737 A088847

Adjacent sequences: A014680 A014681 A014682 * A014684 A014685 A014686

Keyword

nonn,easy

Author

Mohammad K. Azarian

Extensions

More terms from Erich Friedman.

Status

approved