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First differences of A071904 (Odd composite numbers).
3

%I #23 Aug 02 2024 16:56:04

%S 6,6,4,2,6,2,4,6,4,2,4,2,6,2,4,6,2,4,4,2,4,2,2,4,6,6,4,2,2,2,2,2,4,4,

%T 2,6,2,2,2,6,2,4,2,4,4,2,4,2,6,2,2,2,6,6,2,2,2,2,4,2,2,2,2,4,6,4,2,6,

%U 2,2,2,4,2,4,2,4,2,6,2,4,6,2,2,2,4,2,2,2,2,2,4,6,4,2,2,2,2,2,4,2,4,2,2,2,6

%N First differences of A071904 (Odd composite numbers).

%C Are all terms <=6?

%C This is A067970 without its first term. [From _R. J. Mathar_, Aug 17 2009]

%C Yes, all terms are at most 6. For a value of 8, we have to have p, p+2, p+4 all prime, and this is possible only for p=3. As a result, 1 would have to be an odd composite number, which it is not. Therefore all terms are <=6. [From _J. Lowell_, Aug 17 2009]

%o (Python)

%o from sympy import primepi, isprime

%o def A164510(n):

%o m, k = n, primepi(n+1) + n + (n+1>>1)

%o while m != k:

%o m, k = k, primepi(k) + n + (k>>1)

%o for d in range(2, 7, 2):

%o if not isprime(m+d):

%o return d # _Chai Wah Wu_, Aug 02 2024

%Y A071904

%K nonn

%O 1,1

%A _Zak Seidov_, Aug 14 2009