

A157409


Minimum of { k > 0 : [2^n / 3^k] mod 6 = 3 } if such k exists, 0 otherwise.


0



0, 0, 0, 0, 0, 2, 1, 0, 3, 0, 0, 3, 1, 3, 0, 0, 2, 0, 1, 5, 4, 12, 7, 2, 1, 11, 0, 15, 10, 4, 1, 4, 10, 3, 2, 9, 1, 4, 11, 15, 10, 2, 1, 7, 4, 7, 3, 7, 1, 21, 12, 4, 2, 4, 1, 6, 5, 8, 7, 2, 1, 4, 3
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OFFSET

0,6


COMMENTS

It is conjectured that a(n) = 0 only for n in {0,1,2,3,4,7,9,10,14,15,17,26}.
Let N, K defined by: K = max {a(n) for all n <= N}. The following pairs (N : K) for N > 26 mark points where K increases.
(27 : 15), (49 : 21), (110 : 29), (118 : 34), (165 : 58), (2769 : 61), (2837 : 65), (3661 : 70), (14354 : 74), (59913 : 103), (1786453 : 112), (2702893 : 117), (2712849 : 121).


LINKS

Table of n, a(n) for n=0..62.
Peter Luschny, An arithmetic conjecture.


EXAMPLE

a(20) = 4 because MOD([2^20 / 3^4], 6) = 3.


MAPLE

a := proc(m) local l, i, u, A; A := convert(2^m, base, 3); u := 0;
for i from 0 to nops(A)1 do if A[i+1] = 1 then u := u + 1 ;
elif A[i+1] = 0 then if type(u, odd) then RETURN(i) fi fi od;
0 end: seq(a(i), i=0..62);


CROSSREFS

Sequence in context: A194812 A305320 A159813 * A245960 A178616 A165252
Adjacent sequences: A157406 A157407 A157408 * A157410 A157411 A157412


KEYWORD

easy,nonn


AUTHOR

Peter Luschny, Mar 06 2009


STATUS

approved



