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 A160094 a(n) = 1 + A122840(n). 28
 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,10 COMMENTS a(n) is the Levenshtein distance from the decimal expansion of n - 1 to the decimal expansion of n. For example, to convert "9" to "10", substitute "0" for "9" and insert "1". Since two such operations are required, a(10) = 2. See the analogous A091090 (binary expansion) and A115777 (full definition). - Rick L. Shepherd, Mar 25 2015 LINKS Rick L. Shepherd, Table of n, a(n) for n = 1..10000 FORMULA From Hieronymus Fischer, Jun 08 2012: (Start) With m = floor(log_10(n)), frac(x) = x-floor(x): a(n) = Sum_{j=0..m} (1 - ceiling(frac(n/10^j))). a(n) = m + 1 + Sum_{j=1..m} (floor(-frac(n/10^j))). a(n) = 1 + A054899(n) - A054899(n-1). G.f.: g(x) = (x/(1-x)) + Sum_{j>0} x^10^j/(1-x^10^j). (End) Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 10/9. - Amiram Eldar, Jul 10 2023 EXAMPLE a(160) = 2 because the last nonzero digit of 160 (counting from left to right), when 160 is written in base 10, is 6, and that 6 occurs 2 digits from the right in 160. MATHEMATICA IntegerExponent[Range[150]]+1 (* Harvey P. Dale, Feb 06 2015 *) PROG (Other) For(n := 1, n < 10001, Inc(n), Echo(n +> ' ' +> Levenshtein(n-1, n))) Copy the above line into an editing buffer of Notepad++ with the NppCalc plugin installed and ActiveCalc enabled. Position the cursor at the end of the line and press enter to duplicate the contents of this b-file. - Rick L. Shepherd, Mar 25 2015 CROSSREFS Cf. A054899, A055640, A055641, A102669, A122840, A122841, A160093, A196563, A196564, A091090, A115777. Sequence in context: A113607 A351352 A082586 * A043283 A127937 A250209 Adjacent sequences: A160091 A160092 A160093 * A160095 A160096 A160097 KEYWORD base,easy,nonn AUTHOR Anonymous, May 01 2009 EXTENSIONS Name simplified by Jon E. Schoenfield, Feb 26 2014 STATUS approved

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Last modified April 16 03:06 EDT 2024. Contains 371696 sequences. (Running on oeis4.)