OFFSET
1,1
COMMENTS
Equivalently, these are numbers k such that the multiplicative order of 10 modulo k is 10.
These are indices of terms at which 10 appears in A084680.
There are exactly A059892(10) = mu(10/10)*d(10^10-1) + mu(10/5)*d(10^5-1) + mu(10/2)*d(10^2-1) + mu(10/1)*d(10^1-1) = 48 - 12 - 6 + 3 = 33 terms, where d = A000005 and mu = A008683. - Jianing Song, Jun 15 2021
EXAMPLE
1/451 = 0.00221729490022172949002217294900..., whose periodic part is 0022172949.
MATHEMATICA
Select[Range[100000000], MultiplicativeOrder[10, #] == 10 &]
PROG
(PARI) isok(k) = gcd(k, 10) && (znorder(Mod(10, k)) == 10); \\ Michel Marcus, Jun 14 2021
(PARI) my(v=divisors(10^10-1)); select(x->(znorder(Mod(10, x))==10), v) \\ Jianing Song, Jun 15 2021
CROSSREFS
KEYWORD
nonn,base,easy,fini,full
AUTHOR
Tanya Khovanova, Jun 13 2021
EXTENSIONS
a(27)-a(28) from Jinyuan Wang, Jun 13 2021
a(29)-a(33) from Jianing Song, Jun 15 2021
STATUS
approved