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
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
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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
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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