

A117497


Length of shortest sequence b with b(0) = 1, b(i+1) = b(i)+d where db(i) and b(k) = n.


5



0, 1, 2, 2, 3, 3, 4, 3, 4, 4, 5, 4, 5, 5, 5, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 6, 6, 7, 6, 7, 5, 6, 6, 7, 6, 7, 7, 7, 6, 7, 7, 8, 7, 7, 8, 9, 6, 7, 7, 7, 7, 8, 7, 8, 7, 8, 8, 9, 7, 8, 8, 8, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 8, 8, 8, 8, 9, 7, 8, 8, 9, 8, 8, 9, 9, 8, 9, 8, 9, 9, 9, 10, 9, 7, 8, 8, 8, 8, 9, 8, 9, 8, 9
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OFFSET

1,3


COMMENTS

This is similar to the shortest addition chain for n. Both the binary method and the divisor method for finding an addition chain will find a sequence of this type. The smallest few n where there is an addition chain shorter than this sequence are 23,43,46,47,59. The first few n where this sequence is smaller than the shortest addition chain are 143,267,275,286,407. The smallest few n such that a(n) = a(2n) are 86,213,285,342,383.


LINKS

David W. Wilson, Table of n, a(n) for n = 1..10000
Index to sequences related to the complexity of n


FORMULA

a(1)=0, a(n) = 1 + min_{dn, d<n} a(nd).


EXAMPLE

The sequence 1,2,4,8,16,32,64,128,132,143 gets 143 in 9 steps, so a(143) = 9.


CROSSREFS

Cf. A003313, A117498.
Sequence in context: A137813 A003313 A277608 * A117498 A064097 A014701
Adjacent sequences: A117494 A117495 A117496 * A117498 A117499 A117500


KEYWORD

nonn


AUTHOR

Franklin T. AdamsWatters, Mar 22 2006


STATUS

approved



