A113646 a(n) is the smallest composite integer which is >= n.

4, 4, 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

Leroy Quet, Jan 15 2006

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002808, A014683.

Programs

Haskell

a113646 n = if n < 3 then 4 else a014683 n
-- Reinhard Zumkeller, Nov 01 2014

Maple

# This Maple program returns the smallest composite greater than n - N. J. A. Sloane, Sep 11 2019
iscomp := n-> if isprime(n) or (n=1) then false else true; fi;
f := proc(n) local a; global iscomp; a:=n+1; while not iscomp(a) do a:=a+1; od; a; end;

Mathematica

Table[k = n; While[! CompositeQ@ k, k++]; k, {n, 72}] (* Michael De Vlieger, Sep 06 2017 *)

Python

from sympy import isprime
def a(n):
  an = max(4, n)
  while isprime(an): an += 1
  return an
print([a(n) for n in range(1, 73)]) # Michael S. Branicky, Apr 04 2021

Python

from sympy import isprime
def A113646(n): return n+isprime(n) if n>2 else 4 # Chai Wah Wu, Oct 03 2024

Formula

a(1) = a(2) = 4. For n >= 3, a(n) = A014683(n).