A122985 -id:A122985 - cp's OEIS frontend

A122984 Smallest positive composite number, relatively prime to n, such that a(n)+n is also composite.

8, 25, 22, 21, 4, 49, 8, 25, 16, 39, 4, 65, 8, 25, 34, 9, 4, 77, 6, 49, 4, 27, 4, 25, 8, 9, 8, 27, 4, 91, 4, 25, 16, 15, 4, 49, 8, 25, 10, 9, 4, 143, 6, 21, 4, 9, 4, 77, 6, 27, 4, 25, 4, 65, 8, 9, 8, 27, 4, 143, 4, 15, 22, 21, 4, 25, 8, 9, 8, 51, 4, 49, 4, 21, 16, 9, 4, 55, 6, 39, 4, 9, 4, 85

Offset: 1

Franklin T. Adams-Watters, Sep 22 2006

Does not include every composite number; in particular, 12 is not present. If a(n) = 12, gcd(n,12) = 1, but then one of n+4 and n+8 is divisible by 3.

Equals A122985(n) - n. Cf. A096076.

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

Original entry on oeis.org

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

Eric Angelini, Jan 29 2009

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.

Cf. A155874, A122985.

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

More terms from Michael S. Branicky, Apr 09 2021

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A122984 Smallest positive composite number, relatively prime to n, such that a(n)+n is also composite.

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

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