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 A007623 Integers written in factorial base. (Formerly M4678) 226
 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; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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. This concatenated representation is unsatisfactory for large n (above 36287999), when coefficients of 10 or greater start to appear. For these large numbers the representation given in A108731 is better. - N. J. A. Sloane, Jun 04 2012 For n < 10*10!-1, a(n) = concatenation of n-th row of triangle in A108731. - Reinhard Zumkeller, Jun 04 2012 a(n) = A049345(n) for n=0..23. - Reinhard Zumkeller, Jan 05 2014 For n = 36288000 = 10 * 10!, the digits in factorial base are {10, 0, 0, 0, 0, 0, 0, 0, 0, 0}. - Michael De Vlieger, Oct 11 2015, corrected and edited by M. F. Hasler, Nov 27 2018 REFERENCES 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. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS M. F. Hasler (terms 0 .. 1000) & Antti Karttunen, Table of n, a(n) for n = 0..40320 Italo J. Dejter, A numeral system for the middle levels, arXiv:1012.0995 [math.CO], 2010-2015. Italo J. Dejter, Dihedral-symmetry middle-levels problem via a Catalan system of numeration, preprint, 2015. Italo J. Dejter, Ordering the Levels Lk and Lk+1 of B2k+1, preprint, 2015-2017. P. Hecht, Post-Quantum Cryptography: S_381 Cyclic Subgroup of High Order, International Journal of Advanced Engineering Research and Science (IJAERS, 2017) Vol. 4, Issue 6, 78-86. C. A. Laisant, Sur la numération factorielle, application aux permutations, Bulletin de la Société Mathématique de France, 16 (1888), p. 176-183. Wikipedia, Factorial base EXAMPLE a(47) = 1321 because 47 = 1*4! + 3*3! + 2*2! + 1*1! MAPLE a := n -> if nargs<2 then a(n, 2) elif 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[] == 0, dList = Drop[dList, 1]]; dList]; Table[FromDigits[factBaseIntDs[n]], {n, 0, 50}] (* Alonso del Arte, May 03 2006 *) lim = 50; m = 1; While[Factorial@ m < lim, m++]; m; IntegerDigits[#, MixedRadix[Reverse@ Range[2, m]]] & /@ Range@ lim (* Michael De Vlieger, Oct 11 2015, Version 10.2 *) PROG (PARI) apply( a(n, p=2)=if(n

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Last modified February 20 20:08 EST 2020. Contains 332084 sequences. (Running on oeis4.)