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

0,2

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

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

Example

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

Prog

(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

Crossrefs

Cf. A093017-A093029.

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

Sequence in context: A229967 A212049 A212052 * A284493 A337523 A167336

Adjacent sequences: A093015 A093016 A093017 * A093019 A093020 A093021

Keyword

easy,nonn,base

Author

Ray Chandler, Apr 03 2004

Extensions

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

Status

approved