A093029 -id:A093029 - cp's OEIS frontend

A093017 Luhn algorithm double-and-add sum of digits of n.

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

Offset: 0

Ray Chandler, Apr 03 2004

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

			a(18) = 2*1 + 8 = 10.
a(59) = (1+0) + 9 = 10 (1 and 0 are the digits in 10 = 2*5).

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

Cf. A093018-A093029.

Cf. A007953, A093019.

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

def a(n):
    s = str(n)
    r = s[::-1]
    x = sum(int(d) for d in r[::2])
    x += sum(q if (q:=2*int(d)) < 10 else q-9 for d in r[1::2])
    return x
print([a(n) for n in range(87)]) # Michael S. Branicky, Jul 23 2024

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

A093019 a(n) = A093018(n) mod 10.

Original entry on oeis.org

0, 8, 6, 4, 2, 9, 7, 5, 3, 1, 9, 7, 5, 3, 1, 8, 6, 4, 2, 0, 8, 6, 4, 2, 0, 7, 5, 3, 1, 9, 7, 5, 3, 1, 9, 6, 4, 2, 0, 8, 6, 4, 2, 0, 8, 5, 3, 1, 9, 7, 5, 3, 1, 9, 7, 4, 2, 0, 8, 6, 4, 2, 0, 8, 6, 3, 1, 9, 7, 5, 3, 1, 9, 7, 5, 2, 0, 8, 6, 4, 2, 0, 8, 6, 4, 1, 9, 7, 5, 3, 1, 9, 7, 5, 3, 0, 8, 6, 4, 2, 8, 6, 4, 2, 0

Offset: 0

Ray Chandler, Apr 03 2004

Luhn mod 10 check digits of terms in A093018.

			a(1)=8 because A093018(1) mod 10 = 18 mod 10 = 8.
a(5)=9 because A093018(5) mod 10 = 59 mod 10 = 9.

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

Cf. A093017-A093029.

Cf. A010879.

a093019 = flip mod 10 . a093018  -- Reinhard Zumkeller, Nov 08 2014

a(n) = A093018(n) - 10*n. - Reinhard Zumkeller, Nov 08 2014

A093018 Natural numbers with appended Luhn mod 10 check digit.

Original entry on oeis.org

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

Ray Chandler, Apr 03 2004

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

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

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

Cf. A093017-A093029.

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

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

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

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

A093025 Indices of terms in A093019 with value 5.

Original entry on oeis.org

7, 12, 26, 31, 45, 50, 69, 74, 88, 93, 106, 111, 125, 130, 149, 154, 168, 173, 187, 192, 205, 210, 229, 234, 248, 253, 267, 272, 286, 291, 309, 314, 328, 333, 347, 352, 366, 371, 385, 390, 408, 413, 427, 432, 446, 451, 465, 470, 489, 494, 502, 516, 521, 535

Offset: 1

Ray Chandler, Apr 03 2004

Integers which require a following 5 to have a valid Luhn mod 10 check digit.

			12 is in the sequence because A093019(12)=5; 125 has a valid Luhn mod 10 check digit.

Reinhard Zumkeller, Table of n, a(n) for n = 1..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

Cf. A093017-A093029.

a093025 n = a093025_list !! (n-1)
a093025_list = filter ((== 5) . a093019) [0..]
-- Reinhard Zumkeller, Nov 08 2014

A093019(a(n)) = 5. - Reinhard Zumkeller, Nov 08 2014

Offset changed by Reinhard Zumkeller, Nov 08 2014

A093028 Indices of terms in A093019 with value 8.

Original entry on oeis.org

1, 15, 20, 39, 44, 58, 63, 77, 82, 96, 100, 119, 124, 138, 143, 157, 162, 176, 181, 195, 204, 218, 223, 237, 242, 256, 261, 275, 280, 299, 303, 317, 322, 336, 341, 355, 360, 379, 384, 398, 402, 416, 421, 435, 440, 459, 464, 478, 483, 497, 505, 510, 529, 534

Offset: 1

Ray Chandler, Apr 03 2004

Integers which require a following 8 to have a valid Luhn mod 10 check digit.

			15 is in the sequence because A093019(15)=8; 158 has a valid Luhn mod 10 check digit.

Reinhard Zumkeller, Table of n, a(n) for n = 1..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

Cf. A093017-A093029.

a093028 n = a093028_list !! (n-1)
a093028_list = filter ((== 8) . a093019) [0..]
-- Reinhard Zumkeller, Nov 08 2014

A093019(a(n)) = 8. - Reinhard Zumkeller, Nov 08 2014

Offset changed by Reinhard Zumkeller, Nov 08 2014

A093020 Indices of terms in A093019 with value 0.

Original entry on oeis.org

0, 19, 24, 38, 43, 57, 62, 76, 81, 95, 104, 118, 123, 137, 142, 156, 161, 175, 180, 199, 203, 217, 222, 236, 241, 255, 260, 279, 284, 298, 302, 316, 321, 335, 340, 359, 364, 378, 383, 397, 401, 415, 420, 439, 444, 458, 463, 477, 482, 496, 509, 514, 528, 533

Offset: 1

Ray Chandler, Apr 03 2004

Integers which require a following 0 to have a valid Luhn mod 10 check digit.

			19 is in the sequence because A093019(19)=0; 190 has a valid Luhn mod 10 check digit.

Reinhard Zumkeller, Table of n, a(n) for n = 1..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

Cf. A093017-A093029.

a093020 n = a093020_list !! (n-1)
a093020_list = filter ((== 0) . a093019) [0..]
-- Reinhard Zumkeller, Nov 08 2014

A093019(a(n)) = 0. - Reinhard Zumkeller, Nov 08 2014

Offset changed by Reinhard Zumkeller, Nov 08 2014

A093021 Indices of terms in A093019 with value 1.

Original entry on oeis.org

9, 14, 28, 33, 47, 52, 66, 71, 85, 90, 108, 113, 127, 132, 146, 151, 165, 170, 189, 194, 207, 212, 226, 231, 245, 250, 269, 274, 288, 293, 306, 311, 325, 330, 349, 354, 368, 373, 387, 392, 405, 410, 429, 434, 448, 453, 467, 472, 486, 491, 504, 518, 523, 537

Offset: 1

Ray Chandler, Apr 03 2004

Integers which require a following 1 to have a valid Luhn mod 10 check digit.

			14 is in the sequence because A093019(14)=1; 141 has a valid Luhn mod 10 check digit.

Reinhard Zumkeller, Table of n, a(n) for n = 1..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

Cf. A093017-A093029.

a093021 n = a093021_list !! (n-1)
a093021_list = filter ((== 1) . a093019) [0..]
-- Reinhard Zumkeller, Nov 08 2014

A093019(a(n)) = 1. - Reinhard Zumkeller, Nov 08 2014

Offset changed by Reinhard Zumkeller, Nov 08 2014

A093022 Indices of terms in A093019 with value 2.

Original entry on oeis.org

4, 18, 23, 37, 42, 56, 61, 75, 80, 99, 103, 117, 122, 136, 141, 155, 160, 179, 184, 198, 202, 216, 221, 235, 240, 259, 264, 278, 283, 297, 301, 315, 320, 339, 344, 358, 363, 377, 382, 396, 400, 419, 424, 438, 443, 457, 462, 476, 481, 495, 508, 513, 527, 532

Offset: 1

Ray Chandler, Apr 03 2004

Integers which require a following 2 to have a valid Luhn mod 10 check digit.

			18 is in the sequence because A093019(18)=2; 182 has a valid Luhn mod 10 check digit.

Reinhard Zumkeller, Table of n, a(n) for n = 1..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

Cf. A093017-A093029.

a093022 n = a093022_list !! (n-1)
a093022_list = filter ((== 2) . a093019) [0..]
-- Reinhard Zumkeller, Nov 08 2014

A093019(a(n)) = 2. - Reinhard Zumkeller, Nov 08 2014

Offset changed by Reinhard Zumkeller, Nov 08 2014

A093023 Indices of terms in A093019 with value 3.

Original entry on oeis.org

8, 13, 27, 32, 46, 51, 65, 70, 89, 94, 107, 112, 126, 131, 145, 150, 169, 174, 188, 193, 206, 211, 225, 230, 249, 254, 268, 273, 287, 292, 305, 310, 329, 334, 348, 353, 367, 372, 386, 391, 409, 414, 428, 433, 447, 452, 466, 471, 485, 490, 503, 517, 522, 536

Offset: 1

Ray Chandler, Apr 03 2004

Integers which require a following 3 to have a valid Luhn mod 10 check digit.

			13 is in the sequence because A093019(13)=3; 133 has a valid Luhn mod 10 check digit.

Reinhard Zumkeller, Table of n, a(n) for n = 1..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

Cf. A093017-A093029.

a093023 n = a093023_list !! (n-1)
a093023_list = filter ((== 3) . a093019) [0..]
-- Reinhard Zumkeller, Nov 08 2014

A093019(a(n)) = 3. - Reinhard Zumkeller, Nov 08 2014

Offset changed by Reinhard Zumkeller, Nov 08 2014

A093024 Indices of terms in A093019 with value 4.

Original entry on oeis.org

3, 17, 22, 36, 41, 55, 60, 79, 84, 98, 102, 116, 121, 135, 140, 159, 164, 178, 183, 197, 201, 215, 220, 239, 244, 258, 263, 277, 282, 296, 300, 319, 324, 338, 343, 357, 362, 376, 381, 395, 404, 418, 423, 437, 442, 456, 461, 475, 480, 499, 507, 512, 526, 531

Offset: 1

Ray Chandler, Apr 03 2004

Integers which require a following 4 to have a valid Luhn mod 10 check digit.

			17 is in the sequence because A093019(17)=4; 174 has a valid Luhn mod 10 check digit.

Reinhard Zumkeller, Table of n, a(n) for n = 1..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

Cf. A093017-A093029.

a093024 n = a093024_list !! (n-1)
a093024_list = filter ((== 4) . a093019) [0..]
-- Reinhard Zumkeller, Nov 08 2014

A093019(a(n)) = 4. - Reinhard Zumkeller, Nov 08 2014

Offset changed by Reinhard Zumkeller, Nov 08 2014

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A093017 Luhn algorithm double-and-add sum of digits of n.

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A093019 a(n) = A093018(n) mod 10.

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A093018 Natural numbers with appended Luhn mod 10 check digit.

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A093025 Indices of terms in A093019 with value 5.

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A093028 Indices of terms in A093019 with value 8.

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A093020 Indices of terms in A093019 with value 0.

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A093021 Indices of terms in A093019 with value 1.

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