A237042 UPC check digit for n.

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

Offset

1,1

Comments

The UPC check digit is calculated much like a base 10 digital root, except that the digits in the ones place, hundreds place, ten thousands place, etc., are multiplied by 3, before the final step of multiplying the whole sum by -1 prior to taking it modulo 10. Thus the UPC check digit gives the impression of advancing in steps of 7 with each increment of 1 except most of the times when the last digit of n goes from 9 to 0.

References

David Salomon, Coding for Data and Computer Communications. New York: Springer (2006): 41 - 42.

Links

Table of n, a(n) for n=1..96.

GS1, Check Digit Calculator.

Eric Weisstein's World of Mathematics, UPC.

Formula

a(n) = -( (Sum_{i=1..floor(L/2)} d(2i-1)) + 3*(Sum_{j=0..floor(L/2)} d(2j)) ) mod 10, where L is how many digits n has, d(L - 1) is the most significant digit of n, ..., and d(0) is the ones place digit.

Example

a(13) = 0 because 1 * 1 + 3 * 3 = 10, giving a check digit of 0.
a(14) = 7 because 1 * 1 + 4 * 3 = 13, and -13 = 7 mod 10.
a(15) = 4 because 1 * 1 + 5 * 3 = 16, and -16 = 4 mod 10.

Prog

(PARI) a(n) = vecsum(digits(n, 100)*31\-10) % 10; \\ Kevin Ryde, Oct 03 2023

Crossrefs

Cf. A231963, A144468.

Sequence in context: A010508 A070403 A144468 * A258225 A059630 A258330

Adjacent sequences: A237039 A237040 A237041 * A237043 A237044 A237045

Keyword

nonn,easy,base

Author

Alonso del Arte, Feb 02 2014

Status

approved