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A093017 Luhn algorithm double-and-add sum of digits of n. 16
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 7, 8, 9, 10, 11, 12, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Starting on the right, sum digits after doubling alternating digits beginning with the second. If doubled digit >9, reduce by 9 (sum of digits).
a(n) = A007953(A249873(n)); A093019(n) = 10 - a(10*n) mod 10 if less than 10, otherwise 0. - Reinhard Zumkeller, Nov 08 2014
First differences are b(n) defined for n>0 as follows. Take the prime factorization of n and let x be the number of 2's, y be the number of 5's, and z be min(x,y). If z is even, b(n) = 1 - 9*z. If z is odd and y=z, b(n) = 2 - 9*z. If z is odd and y>z, b(n) = -7 - 9*z. Now a(n) = a(n-1) + b(n). - Mathew Englander, Aug 04 2021
LINKS
John Kilgo, Using the Luhn Algorithm, DotNetJohn.com.
Webopedia, Luhn formula
Wikipedia, Luhn algorithm
FORMULA
a(0)=0; for n not divisible by 10, a(n)=1+a(n-1); for n divisible by 10 but not 50, a(n)=2+a(n-10); for n divisible by 50 but not 100, a(n)=1+a(n-50); for n divisible by 100, a(n)=a(n/100). - Mathew Englander, Aug 04 2021
EXAMPLE
a(18) = 2*1 + 8 = 10.
a(59) = (1+0) + 9 = 10 (1 and 0 are the digits in 10 = 2*5).
PROG
(Haskell)
a093017 n = if n == 0 then 0 else a093017 n' + a007953 (2 * t) + d
where (n', td) = divMod n 100; (t, d) = divMod td 10
-- Reinhard Zumkeller, Nov 08 2014
CROSSREFS
Sequence in context: A189506 A173529 A273005 * A156230 A028897 A244158
KEYWORD
easy,nonn,base
AUTHOR
Ray Chandler, Apr 03 2004
STATUS
approved

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Last modified May 22 05:20 EDT 2024. Contains 372742 sequences. (Running on oeis4.)