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A060318
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Powers of 3 in the odd Catalan numbers cat[2^n-1].
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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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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 ]).
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EXAMPLE
| a(5)=0 because 2^5-1= 31 and cat[31]= 7.11.17.19.37.41.43.47.53.59.61 so the power of 3 is zero.
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MATHEMATICA
| pow3[ nfac_ ] := (nfac - Plus @@ IntegerDigits[ nfac, 3 ])/(3-1) powcat3[ n_ ] := pow3[ 2n ]-pow3[ n+1 ]-pow3[ n ]; Table[ powcat3[ 2^n-1 ], {n, 2048} ]
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CROSSREFS
| Cf. A000108, A048896, A048881.
Sequence in context: A128097 A173662 A172026 * A089994 A178107 A100260
Adjacent sequences: A060315 A060316 A060317 * A060319 A060320 A060321
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KEYWORD
| nonn
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AUTHOR
| Wouter Meeussen (wouter.meeussen(AT)pandora.be), Mar 28 2001
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