A137385 - OEIS

%I #12 Apr 22 2020 16:59:09

%S 8190,7600,2184,6810,7246,2024,994,5956,182,7128,336,1806,448,920,

%T 1932,5068,375,168,330,6578,196,312,274,1579,6250,414,0,821,200,1908,

%U 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

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

%C The most frequent errors are:

%C - permutation between 2 ranks

%C - error in one rank

%H Author?, <a href="http://les-mathematiques.u-strasbg.fr/phorum5/read.php?2,439164,439164#msg-439164">Les-mathematiques.net</a> [Broken link?]

%e Actual n is 97. It generates 74 errors.

%e Best choices could be 27, 54, 63, 81 or 99 instead of 97.

%o (Python)

%o for cle in range(1,100):

%o     n=0

%o     for r1 in range(1,14):

%o         for r2 in range(r1,14):

%o             ur1=cle-(10**(13-r1))%cle

%o             ur2=cle-(10**(13-r2))%cle

%o             for c1 in range(10):

%o                 for c2 in range(10):

%o                     if c1==c2:

%o                         dif=1

%o                     else:

%o                         dif=(c1*ur1-c2*ur2)%cle

%o                     if dif==0:

%o                         n=n+1

%o     print(cle,':',n)

%K fini,full,nonn

%O 1,1

%A _Sébastien Dumortier_, Apr 26 2008