A155875 Smallest positive composite number such that a(n) - n is also composite.

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

Offset: 0

Author

Eric Angelini, Jan 29 2009

Keywords

• base
• easy
• nonn

Comments

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 composite; subtracting n = 2 from a(2) gives 6-2 = 4 which is composite; subtracting n = 3 from a(3) gives 9-3 = 6 which is composite; etc.

Crossrefs

Cf. A155874, A122985.

Programs

Python

from sympy import isprime
def composite(n): return n >= 4 and not isprime(n)
def a(n):
  an = n + 4
  while not (composite(an) and composite(an-n)): an += 1
  return an
print([a(n) for n in range(67)]) # Michael S. Branicky, Apr 09 2021

Extensions

More terms from Michael S. Branicky, Apr 09 2021