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

Author

Alonso del Arte, Feb 02 2014

Keywords

• nonn
• easy
• base

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.

Examples

			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.
		

References

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

Links

• GS1, Check Digit Calculator.
• Eric Weisstein's World of Mathematics, UPC.

Crossrefs

Cf. A231963, A144468.

Programs

PARI

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

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.