id:A034968 - OEIS Search Results

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Minimal number of factorials which add to n.

+0
5

0, 1, 1, 2, 2, 3, 1, 2, 2, 3, 3, 4, 2, 3, 3, 4, 4, 5, 3, 4, 4, 5, 5, 6, 1, 2, 2, 3, 3, 4, 2, 3, 3, 4, 4, 5, 3, 4, 4, 5, 5, 6, 4, 5, 5, 6, 6, 7, 2, 3, 3, 4, 4, 5, 3, 4, 4, 5, 5, 6, 4, 5, 5, 6, 6, 7, 5, 6, 6, 7, 7, 8, 3, 4, 4, 5, 5, 6, 4, 5, 5, 6, 6, 7, 5, 6, 6, 7, 7, 8, 6, 7, 7, 8, 8, 9, 4, 5, 5, 6, 6, 7, 5, 6, 6, 7 (list; graph; listen)

	OFFSET	`0,4`
	COMMENT	`Equivalently, sum of digits when n is written in factorial base (A007623).` `Also minimum number of adjacent transpositions needed to produce each permutation in the list A055089 (or number of swappings needed to bubble sort each such permutation).`
	FORMULA	`a(n)=n-sum(i>=2, (i-1)*floor(n/i!)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 26 2003`
	EXAMPLE	`a(205=1!1+3!2+4!3+5!1)=1+2+3+1=6.`
	MAPLE	[seq(convert(fac_base(j), `+`), j=0..119)]; # fac_base and PermRevLexUnrank given in A055089. Perm2InversionVector in A064039 Or alternatively: [seq(convert(Perm2InversionVector(PermRevLexUnrank(j)), `+`), j=0..119)];
	CROSSREFS	`Partial sums of first n! terms: A001809. See A055091 for the minimum number of any transpositions. A034968[A056019[n]] = A034968[n] for all n.` `Sequence in context: A097028 A092331 A089293 this_sequence A054707 A055460 A067514` `Adjacent sequences: A034965 A034966 A034967 this_sequence A034969 A034970 A034971`
	KEYWORD	`nonn`
	AUTHOR	`Erich Friedman (erich.friedman(AT)stetson.edu)`
	EXTENSIONS	`Additional comments from Antti Karttunen, Aug 23, 2001.`

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Last modified July 25 07:41 EDT 2008. Contains 142293 sequences.

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