A093018 - OEIS

%I #18 Jul 23 2024 18:06:23

%S 0,18,26,34,42,59,67,75,83,91,109,117,125,133,141,158,166,174,182,190,

%T 208,216,224,232,240,257,265,273,281,299,307,315,323,331,349,356,364,

%U 372,380,398,406,414,422,430,448,455,463,471,489,497,505,513,521,539

%N Natural numbers with appended Luhn mod 10 check digit.

%C Indices of terms in A093017 == 0 mod 10.

%C A249832(a(n)) = 1; A093017(a(n)) mod 10 = 0; a(n) = 10*n + A093019(n); A093019(n) = a(n) mod 10. - _Reinhard Zumkeller_, Nov 08 2014

%C The sequence includes all Canadian Social Insurance Numbers, as well as all modern credit and debit card numbers. - _Mathew Englander_, Aug 04 2021

%H Reinhard Zumkeller, <a href="/A093018/b093018.txt">Table of n, a(n) for n = 0..10000</a>

%H John Kilgo, DotNetJohn.com, <a href="http://www.dotnetjohn.com/articles/articleid97.aspx">Using the Luhn Algorithm</a>

%H Webopedia, <a href="http://www.webopedia.com/TERM/L/Luhn_formula.html">Luhn formula</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Luhn_algorithm">Luhn algorithm</a>

%H <a href="/index/De#decimal_expansion">Index entries for sequences related to decimal expansion of n</a>

%e 18 is in the sequence because A093017(18)=10 == 0 mod 10.

%e 59 is in the sequence because A093017(59)=10 == 0 mod 10.

%o (Haskell)

%o a093018 n = a093018_list !! n

%o a093018_list = filter ((== 1) . a249832) [0..]

%o -- _Reinhard Zumkeller_, Nov 08 2014

%o (Python)

%o def a(n):

%o     s = str(n)

%o     r = s[::-1]

%o     x = sum(int(d) for d in r[1::2])

%o     x += sum(q if (q:=2*int(d)) < 10 else q-9 for d in r[::2])

%o     x = x%10

%o     c = str((10 - x) if x > 0 else 0)

%o     return int(s+c)

%o print([a(n) for n in range(54)]) # _Michael S. Branicky_, Jul 23 2024

%Y Cf. A093017-A093029.

%Y Cf. A249832, A093017, A249830 (complement), A249854, A249855, A010879.

%K easy,nonn,base

%O 0,2

%A _Ray Chandler_, Apr 03 2004

%E Original name end comment interchanged by _Reinhard Zumkeller_, Nov 08 2014