A155874 -id:A155874 - cp's OEIS frontend

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

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

A155878 a(0)=4; for n > 0, a(n) is the smallest composite number c > a(n-1) such that c + n is also composite.

Original entry on oeis.org

4, 8, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 35, 36, 39, 40, 42, 44, 45, 46, 48, 49, 51, 52, 54, 55, 57, 58, 60, 62, 63, 64, 65, 66, 69, 70, 72, 74, 75, 76, 77, 78, 80, 82, 84, 86, 87, 88, 90, 91, 93, 94, 95, 96, 98, 99, 102, 104, 105, 106, 108

Offset: 0

Eric Angelini, Jan 29 2009

			a(0)=4. Adding a(0) to n=0 gives 4+0=4, which is a composite number; adding a(1) to n=1 gives 8+1=9 which is composite; adding a(2) to n=2 gives 10+2=12 which is composite; adding a(3) to n=3 gives 12+3=15 which is composite; etc.

Cf. A155874.

isA002808 := proc(n) option remember; RETURN(n>= 4 and not isprime(n)) ; end: A155878:= 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(A155878(n),n=0..100) ; # R. J. Mathar, Jan 31 2009

Extended by R. J. Mathar, Jan 31 2009

Name edited by Jon E. Schoenfield, Jan 20 2019

cp's OEIS Frontend

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

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