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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 Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 John Kilgo, Using the Luhn Algorithm, DotNetJohn.com. Webopedia, Luhn formula Wikipedia, Luhn algorithm Index entries for sequences related to decimal expansion of n 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 Cf. A093018-A093029. Cf. A007953, A093019. Sequence in context: A189506 A173529 A273005 * A156230 A028897 A244158 Adjacent sequences: A093014 A093015 A093016 * A093018 A093019 A093020 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.)