A155879 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

LINKS

Table of n, a(n) for n=0..68.

EXAMPLE

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.

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

PROG

(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