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%I #20 Jul 19 2014 14:38:19
%S 1,5,7,7,11,5,7,7,11,1,1,7,5,5,1,11,7,1,1,5,11,11,7,5,11,1,1,5,11,1,1,
%T 5,7,7,5,5,11,11,7,5,1,7,11,5,7,7,7,7,11,5,7,11,5,1,11,7,5,5,11,1,1,
%U 11,11,7,1,11,11,5
%N (First arithmetic derivative of primorials) read mod 12.
%C A024451 as numerator of Sum_{i = 1..n} 1/prime(i) is the first arithmetic derivative of primorials prime(n)# of A002110. a(n) shows the distribution of A024451 over four residual classes.
%F a(n) = (prime(n)#)' mod 12 or a(n) = A024451(n) mod 12.
%e a(4) = [(prime(4)#)' = (4#)' = (210)' = 247] mod 12 = 7,
%e a(6) = [(prime(6)#)' = (13#)' = (30030)' = 40361] mod 12 = 5.
%o (PARI) a(n) = numerator(sum(i=1, n, 1/prime(i))) % 12; \\ _Michel Marcus_, Jul 07 2014
%Y Cf. A002110, A024451, A003415, A244622.
%K nonn
%O 1,2
%A _Freimut Marschner_, Jul 02 2014
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