A093018 Natural numbers with appended Luhn mod 10 check digit.

0, 18, 26, 34, 42, 59, 67, 75, 83, 91, 109, 117, 125, 133, 141, 158, 166, 174, 182, 190, 208, 216, 224, 232, 240, 257, 265, 273, 281, 299, 307, 315, 323, 331, 349, 356, 364, 372, 380, 398, 406, 414, 422, 430, 448, 455, 463, 471, 489, 497, 505, 513, 521, 539

Offset: 0

Author

Ray Chandler, Apr 03 2004

Keywords

• easy
• nonn
• base

Comments

Indices of terms in A093017 == 0 mod 10.

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

The sequence includes all Canadian Social Insurance Numbers, as well as all modern credit and debit card numbers. - Mathew Englander, Aug 04 2021

Examples

			18 is in the sequence because A093017(18)=10 == 0 mod 10.
59 is in the sequence because A093017(59)=10 == 0 mod 10.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• John Kilgo, DotNetJohn.com, Using the Luhn Algorithm
• Webopedia, Luhn formula
• Wikipedia, Luhn algorithm
• Index entries for sequences related to decimal expansion of n

Crossrefs

Cf. A093017-A093029.

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

Programs

Haskell

a093018 n = a093018_list !! n
a093018_list = filter ((== 1) . a249832) [0..]
-- Reinhard Zumkeller, Nov 08 2014

Python

def a(n):
    s = str(n)
    r = s[::-1]
    x = sum(int(d) for d in r[1::2])
    x += sum(q if (q:=2*int(d)) < 10 else q-9 for d in r[::2])
    x = x%10
    c = str((10 - x) if x > 0 else 0)
    return int(s+c)
print([a(n) for n in range(54)]) # Michael S. Branicky, Jul 23 2024

Extensions

Original name end comment interchanged by Reinhard Zumkeller, Nov 08 2014