A343447 Smallest m such that alternating integer 101...101 = A094028(m) is a multiple of A045572(n), (i.e., integers coprime with 10).

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).

Links

Table of n, a(n) for n=1..70.

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

Cf. A030141, A045572, A052983, A094028, A099679.

Sequence in context: A121098 A121094 A029595 * A320138 A325102 A275436

Adjacent sequences: A343444 A343445 A343446 * A343448 A343449 A343450

Keyword

nonn,base

Author

Bernard Schott, Apr 15 2021

Extensions

More terms from Felix Fröhlich, Apr 15 2021

Status

approved