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Search: id:A007623
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| A007623 |
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Integers written in factorial base.
(Formerly M4678)
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+0
29
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| 0, 1, 10, 11, 20, 21, 100, 101, 110, 111, 120, 121, 200, 201, 210, 211, 220, 221, 300, 301, 310, 311, 320, 321, 1000, 1001, 1010, 1011, 1020, 1021, 1100, 1101, 1110, 1111, 1120, 1121, 1200, 1201, 1210, 1211, 1220, 1221, 1300, 1301, 1310, 1311, 1320, 1321, 2000, 2001, 2010
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Places reading from right have values (1, 2, 6, 24, 120, ...) = factorials.
Also the reversed inversion vectors for the list of all finite permutations in reversed lexicographic order: A055089.
For large n it would be better to separate the "digits" by commas. - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Mar 27 2007
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 2, p. 192.
F. Smarandache, Definitions solved and unsolved problems, conjectures and theorems in number theory and geometry, edited by M. Perez, Xiquan Publishing House, 2000.
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LINKS
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M. F. Hasler, Table of n, a(n) for n = 0..1000
F. Smarandache, Definitions, Solved and Unsolved Problems, Conjectures, ...
Wikipedia, Factorial base
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EXAMPLE
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a(47) = 1321 because 47 = 1*4! + 3*3! + 2*2! + 1*1!
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MAPLE
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a := n -> if nargs<2 then a(n, 2) elif n<args[2] then n else a(iquo(n, args[2]), args[2]+1)*10+irem(n, args[2]) fi: 'a(i)'$i=0..200;
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MATHEMATICA
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factBaseIntDs[n_] := Module[{m, i, len, dList, currDigit}, i = 1; While[n > i!, i++ ]; m = n; len = i; dList = Table[0, {len}]; Do[ currDigit = 0; While[m >= j!, m = m - j!; currDigit++ ]; dList[[len - j + 1]] = currDigit, {j, i, 1, -1}]; If[dList[[1]] == 0, dList = Drop[dList, 1]]; dList]; Table[FromDigits[factBaseIntDs[n]], {n, 0, 50}] - Alonso Delarte (alonso.delarte(AT)gmail.com), May 03 2006
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PROGRAM
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(PARI): a(n, p=2) = if( n<p, n, a( n\p, p+1 )*10 + n%p ); vector(200, i, a(i-1)) - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Mar 27 2007
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CROSSREFS
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Cf. A000142. See also primorial base A049345, sum of digits A034968, number of nonzero digits A060130. Simple algorithm fac_base given in A055089.
Cf. A060112, A060495. Permutation of A064039.
Sequence in context: A037307 A165265 A049345 this_sequence A109827 A109839 A087486
Adjacent sequences: A007620 A007621 A007622 this_sequence A007624 A007625 A007626
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KEYWORD
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base,nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com), Mira Bernstein (mira(AT)math.berkeley.edu)
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EXTENSIONS
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More terms from R. K. Guy (rkg(AT)cpsc.ucalgary.ca)
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