VOOZH about

URL: https://oeis.org/A343447

⇱ A343447 - OEIS

login
A343447
Smallest m such that alternating integer 101...101 = A094028(m) is a multiple of A045572(n), (i.e., integers coprime with 10).
0
0, 2, 2, 8, 10, 2, 7, 8, 2, 10, 26, 13, 14, 32, 2, 2, 4, 20, 22, 20, 23, 12, 8, 28, 29, 8, 32, 32, 34, 3, 32, 12, 80, 40, 41, 21, 2, 14, 47, 98, 1, 16, 52, 53, 2, 55, 8, 23, 120, 14, 20, 20, 64, 8, 3, 22, 68, 32, 20, 73, 74, 71, 38, 38, 32, 80, 82, 38, 8, 42
OFFSET
1,2
COMMENTS
Every number coprime with 10 has a smallest multiple that is repunit (A099679).
Every positive number has a smallest multiple consisting of a succession of 1's followed by a succession of 0's (A052983).
Every number coprime with 10 has a smallest multiple that is alternating of the form 1010...0101 (this sequence).
EXAMPLE
A045572(3) = 7, the smallest alternating multiple of 7 in A094028 is A094028(2) = 10101 because 1443*7 = 10101, as 1 and 101 are not divisible by 7, so a(3) = 2.
MATHEMATICA
a[n_] := Module[{k = (5*n + (Mod[3*n + 2, 4] - 4))/2, m = 0}, While[! Divisible[1 + 100*(100^m - 1)/99, k], m++]; m]; Array[a, 100] (* Amiram Eldar, Apr 15 2021 *)
PROG
(PARI) a045572(n)=10*(n>>2)+[-1, 1, 3, 7][n%4+1] \\ after Charles R Greathouse IV in A045572
a094028(n) = 1+100*(100^n-1)/99
a(n) = for(m=0, oo, if(a094028(m)%a045572(n)==0, return(m))) \\ Felix Fröhlich, Apr 15 2021
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Apr 15 2021
EXTENSIONS
More terms from Felix Fröhlich, Apr 15 2021
STATUS
approved