A137385 Number of errors that occur when choosing n as modulus in French INSEE code (0<n<100).

8190, 7600, 2184, 6810, 7246, 2024, 994, 5956, 182, 7128, 336, 1806, 448, 920, 1932, 5068, 375, 168, 330, 6578, 196, 312, 274, 1579, 6250, 414, 0, 821, 200, 1908, 244, 4246, 84, 342, 878, 154, 112, 301, 140, 5844, 134, 182, 122, 276, 168, 255, 111, 1347, 125, 6248, 92, 363, 104, 0, 294, 715, 85, 183, 75, 1758, 92, 223, 0, 3492, 392, 78, 70, 300, 64, 864, 110, 140, 63, 108, 1673, 262, 28, 130, 65, 5054, 0, 120, 63, 160, 323, 111, 51, 238, 57, 168, 28, 225, 77, 102, 286, 1132, 74, 120, 0

Offset

1,1

Comments

The most frequent errors are:

- permutation between 2 ranks

- error in one rank

Links

Table of n, a(n) for n=1..99.

Author?, Les-mathematiques.net [Broken link?]

Example

Actual n is 97. It generates 74 errors.
Best choices could be 27, 54, 63, 81 or 99 instead of 97.

Prog

(Python)
for cle in range(1, 100):
    n=0
    for r1 in range(1, 14):
        for r2 in range(r1, 14):
            ur1=cle-(10**(13-r1))%cle
            ur2=cle-(10**(13-r2))%cle
            for c1 in range(10):
                for c2 in range(10):
                    if c1==c2:
                        dif=1
                    else:
                        dif=(c1*ur1-c2*ur2)%cle
                    if dif==0:
                        n=n+1
    print(cle, ':', n)

Crossrefs

Sequence in context: A235095 A283954 A250939 * A108093 A051334 A145592

Adjacent sequences: A137382 A137383 A137384 * A137386 A137387 A137388

Keyword

fini,full,nonn

Author

Sébastien Dumortier, Apr 26 2008

Status

approved