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 A060318 Powers of 3 in the odd Catalan numbers cat[2^n-1]. 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 (list; graph; refs; listen; history; text; internal format)
 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 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. 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} ] 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

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Last modified January 22 19:44 EST 2020. Contains 331153 sequences. (Running on oeis4.)