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Smallest positive composite number such that a(n) - n is also composite.
1

%I #6 Apr 09 2021 14:41:48

%S 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,

%T 33,30,33,32,33,34,35,36,39,38,39,40,45,42,45,44,45,46,49,48,49,50,51,

%U 52,55,54,55,56,57,58,63,60,63,62,63,64,65,66,69,68,69,70

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

%C 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.

%o (Python)

%o from sympy import isprime

%o def composite(n): return n >= 4 and not isprime(n)

%o def a(n):

%o an = n + 4

%o while not (composite(an) and composite(an-n)): an += 1

%o return an

%o print([a(n) for n in range(67)]) # _Michael S. Branicky_, Apr 09 2021

%Y Cf. A155874, A122985.

%K base,easy,nonn

%O 0,1

%A _Eric Angelini_, Jan 29 2009

%E More terms from _Michael S. Branicky_, Apr 09 2021