

A064631


4^n = x*3^n+y*2^n+z*1^n, so 4^n equals the sum of a(n)=x+y+z pieces of like powers (=length of right side of solution of this Diophantine equation). Length of solutions obtained with "greedy algorithm" are given in A064630[n]. Here the binary order [A029837] of the length of those solutions is displayed, which "on the average" nearly equals n.


3



1, 3, 3, 4, 5, 4, 7, 7, 8, 10, 11, 12, 13, 14, 15, 16, 16, 16, 18, 18, 20, 22, 21, 23, 25, 25, 24, 28, 27, 29, 31, 32, 33, 34, 35, 36, 37, 37, 39, 40, 39, 42, 42, 44, 44, 46, 46, 46, 49, 50, 51, 51, 51, 54, 55, 55, 57, 57, 59, 60, 60, 61, 63, 64, 64, 66, 60, 62, 67, 70, 69, 72
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OFFSET

1,2


COMMENTS

a(n)<=n and near to n.
a(n)=n for n = {1, 3, 4, 5, 7, 10, 11, 12, 13, 14, 15, 16, 22, 25, 28, 31, 32, 33, 34, 35, 36, 37, 39, 40, 42, 44, 46, 49, 50, 51, 54, 55, 57, 59, 60, 63, 64, 66, 70, 72, 75, 78, 79, 82, 87, 88, 89, 90, 93, 94, 95, 97, 98, 99, 100}.


LINKS

Table of n, a(n) for n=1..72.


FORMULA

a(n) = A029837(A064630(n)) = ceiling(log_2(A064630(n)).


CROSSREFS

Cf. A002379, A002380, A060692, A064628, A064629, A064630, A029837.
Sequence in context: A196314 A196287 A196337 * A298200 A072648 A185585
Adjacent sequences: A064628 A064629 A064630 * A064632 A064633 A064634


KEYWORD

nonn


AUTHOR

Labos Elemer, Oct 01 2001


STATUS

approved



