

A060318


Powers of 3 in the odd Catalan numbers cat[2^n1].


0



0, 0, 1, 2, 0, 1, 3, 0, 3, 3, 3, 6, 2, 2, 9, 5, 5, 4, 8, 5, 9, 10, 5, 4, 4, 4, 9, 9, 8, 11, 13, 13, 10, 11, 10, 8, 6, 12, 13, 14, 13, 11, 14, 15, 16, 13, 11, 10, 12, 18, 20, 19, 20, 11, 13, 19, 22, 18, 15, 26, 20, 17, 17, 26, 21, 22, 18, 18, 23, 26, 20, 19, 23, 21, 22, 19, 27, 17, 35
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OFFSET

1,4


COMMENTS

Conjecture: all odd Catalan numbers have smallest factor 3, except cat[3] has smallest divisor 5 and cat[31] and cat[255] have smallest divisor 7 (checked up to cat[ 1+2^2048 ]).


LINKS

Table of n, a(n) for n=1..79.


EXAMPLE

a(5)=0 because 2^51= 31 and cat[31]= 7.11.17.19.37.41.43.47.53.59.61 so the power of 3 is zero.


MATHEMATICA

pow3[ nfac_ ] := (nfac  Plus @@ IntegerDigits[ nfac, 3 ])/(31) powcat3[ n_ ] := pow3[ 2n ]pow3[ n+1 ]pow3[ n ]; Table[ powcat3[ 2^n1 ], {n, 2048} ]


CROSSREFS

Cf. A000108, A048896, A048881.
Sequence in context: A257230 A172026 A296046 * A246061 A263730 A331533
Adjacent sequences: A060315 A060316 A060317 * A060319 A060320 A060321


KEYWORD

nonn


AUTHOR

Wouter Meeussen, Mar 28 2001


STATUS

approved



