A244621 (First arithmetic derivative of primorials) read mod 12.

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, 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, 11, 11, 7, 1, 11, 11, 5

Offset: 1

Author

Freimut Marschner, Jul 02 2014

Keywords

• nonn

Comments

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.

Examples

			a(4) = [(prime(4)#)' = (4#)' = (210)' = 247] mod 12 = 7,
a(6) = [(prime(6)#)' = (13#)' = (30030)' = 40361] mod 12 = 5.
		

Crossrefs

Cf. A002110, A024451, A003415, A244622.

Programs

PARI

a(n) = numerator(sum(i=1, n, 1/prime(i))) % 12; \\ Michel Marcus, Jul 07 2014

Formula

a(n) = (prime(n)#)' mod 12 or a(n) = A024451(n) mod 12.