id:A060318 - OEIS Search Results

Search: id:A060318

Displaying 1-1 of 1 results found.

page 1

Powers of 3 in the odd Catalan numbers cat[2^n-1].

+0
1

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; listen)

	OFFSET	`1,4`
	COMMENT	`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 ]).`
	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: A029297 A022880 A128097 this_sequence A089994 A100260 A165317` `Adjacent sequences: A060315 A060316 A060317 this_sequence A060319 A060320 A060321`
	KEYWORD	`nonn`
	AUTHOR	`Wouter Meeussen (wouter.meeussen(AT)pandora.be), Mar 28 2001`

page 1

Search completed in 0.003 seconds

Last modified November 24 23:16 EST 2009. Contains 167481 sequences.

AT&T Labs Research