

A119674


Number of states of the minimal deterministic finite automaton that accepts binary strings that represent numbers that are divisible by n.


0



1, 2, 3, 3, 5, 4, 7, 4, 9, 6, 11, 5, 13, 8, 15, 5, 17, 10, 19, 7, 21, 12, 23, 6, 25, 14, 27, 9, 29, 16, 31, 6, 33, 18, 35, 11, 37, 20, 39, 8, 41, 22, 43, 13, 45, 24, 47, 7, 49, 26, 51, 15, 53, 28, 55, 10, 57, 30, 59, 17, 61, 32, 63, 7, 65, 34, 67, 19, 69, 36, 71, 12, 73, 38, 75, 21, 77
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OFFSET

1,2


COMMENTS

a(n) = n for all odd n.


LINKS

Table of n, a(n) for n=1..77.


FORMULA

Recurrence: a(1)=1; then a(2n)=a(n)+1, a(2n+1)=2n+1.  Benoit Cloitre, Jun 04 2007
a(n) = A000265(n) + A007814(n) = n/2^A007814(n) + A007814(n).  Ralf Stephan, Jul 07 2013


EXAMPLE

a(12) = 5.


PROG

(PARI) a(n)=n/2^valuation(n, 2)+valuation(n, 2)  Ralf Stephan, Jul 07 2013
(PARI) a(n)=if(n<2, 1, if(n%2, n, a(n/2)+1))  Benoit Cloitre, Jun 04 2007


CROSSREFS

Sequence in context: A135533 A296075 A318678 * A064920 A064916 A062854
Adjacent sequences: A119671 A119672 A119673 * A119675 A119676 A119677


KEYWORD

nonn


AUTHOR

Mirko Rahn (rahn(AT)ira.uka.de), Jun 12 2006


STATUS

approved



