A072970 Least k > 0 such that the last digit of k^n is the same as the last digit of n*k.

1, 2, 5, 4, 5, 6, 5, 2, 5, 10, 1, 8, 5, 4, 5, 6, 5, 8, 2, 10, 1, 2, 5, 4, 5, 6, 5, 2, 5, 10, 1, 8, 5, 4, 5, 6, 5, 8, 2, 10, 1, 2, 5, 4, 5, 6, 5, 2, 5, 10, 1, 8, 5, 4, 5, 6, 5, 8, 2, 10, 1, 2, 5, 4, 5, 6, 5, 2, 5, 10, 1, 8, 5, 4, 5, 6, 5, 8, 2, 10, 1, 2, 5, 4, 5, 6, 5, 2, 5, 10, 1, 8, 5, 4, 5, 6, 5, 8, 2

Offset

1,2

Links

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

Formula

a(n) is a periodic sequence with period (1, 2, 5, 4, 5, 6, 5, 2, 5, 10, 1, 8, 5, 4, 5, 6, 5, 8, 2, 10) of length 20

a(n)=(1/3800)*{1809*(n mod 20) - 1421*[(n + 1) mod 20] + 1239*[(n + 2) mod 20] - 471*[(n + 3) mod 20] + 289*[(n + 4) mod 20] - 91*[(n + 5) mod 20] - 91*[(n + 6) mod 20] + 289*[(n + 7) mod 20] + 669*[(n + 8) mod 20] - 1231*[(n + 9) mod 20] + 1809*[(n + 10) mod 20] - 851*[(n + 11) mod 20] - 471*[(n + 12) mod 20] + 669*[(n + 13) mod 20] + 289*[(n + 14) mod 20] - 91*[(n + 15) mod 20] - 91*[(n + 16) mod 20] + 289*[(n + 17) mod 20] - 471*[(n + 18) mod 20] - 91*[(n + 19) mod 20]}, with n>=0 - Paolo P. Lava, Jun 11 2007

Mathematica

kld[n_]:=Module[{k=1}, While[PowerMod[k, n, 10]!=Mod[n*k, 10], k++]; k]; Array[kld, 100] (* Harvey P. Dale, Sep 08 2012 *)

Prog

(PARI) a(n)=if(n<0, 0, k=1; while(abs(k^n%10-(n*k)%10)>0, s++); s)

Crossrefs

Sequence in context: A235052 A102066 A279404 * A276320 A011036 A086267

Adjacent sequences: A072967 A072968 A072969 * A072971 A072972 A072973

Keyword

base,easy,nonn

Author

Benoit Cloitre, Aug 13 2002

Status

approved