A155879 a(0) = 4; for n > 0, a(n) is the smallest composite number c > a(n-1) such that c - n is also composite.

4, 9, 10, 12, 14, 15, 16, 21, 22, 24, 25, 26, 27, 28, 30, 33, 34, 35, 36, 39, 40, 42, 44, 45, 46, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 104, 105, 106, 108

Offset: 0

Author

Eric Angelini, Jan 29 2009

Keywords

• base
• easy
• nonn

Examples

			a(0) = 4. Subtracting n = 0 from a(0) gives 4-0 = 4, which is a composite number; subtracting n = 1 from a(1) gives 9-1 = 8, which is a composite number; subtracting n = 2 from a(2) gives 12-2 = 10, which is a composite number; subtracting n = 3 from a(3) gives 15-3 = 12, which is a composite number; etc.
		

Crossrefs

Cf. A155875.

Programs

Maple

isA002808 := proc(n) option remember; RETURN(n>= 4 and not isprime(n)) ; end: A155879:= proc(n) option remember; local a; if n = 0 then 4; else for a from procname(n-1)+1 do if isA002808(a) and isA002808(a-n) then RETURN(a) ; fi; od: fi; end: seq(A155879(n),n=0..100) ; # R. J. Mathar, Jan 31 2009

Python

from sympy import isprime
def composite(n): return n >= 4 and not isprime(n)
def aupton(nn):
  alst = [4]
  for n in range(1, nn+1):
    an = max(alst[-1] + 1, n + 4)
    while not (composite(an) and composite(an-n)): an += 1
    alst.append(an)
  return alst
print(aupton(68)) # Michael S. Branicky, Apr 09 2021

Extensions

Corrected from a(2) on by R. J. Mathar, Jan 31 2009

Name edited by Jon E. Schoenfield, Jan 19 2019