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

Author

Mohammad K. Azarian

Keywords

• nonn
• easy

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

Crossrefs

Cf. A010051, A113646, A380457.

Programs

Haskell

a014683 n = n + a010051' n  -- Reinhard Zumkeller, Nov 01 2014

Mathematica

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

PARI

a(n)=n+isprime(n)

Python

from sympy import isprime
def A014683(n): return n+isprime(n) # Chai Wah Wu, Oct 03 2024

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

Extensions

More terms from Erich Friedman.