A178836 Numbers n such that the period of 1/n equals the period of 1/R(n), where R(n) (A004086) is the reversal of n.

3, 7, 9, 11, 33, 77, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 707, 717, 727, 737, 747, 757, 767, 777, 787, 797, 909, 919, 929, 939, 949, 959, 969, 979, 989, 999, 1001, 1111, 1221, 1331, 1441, 1551

Offset

1,1

Comments

Non-palindromic numbers are included in this sequence :

{3267, 3927, 7293, 7632,...}

Links

Table of n, a(n) for n=1..53.

Example

3267 is in the sequence because period (1/3267) = 66 and also period(1/7623) = 66.
3927 is in the sequence because period (1/3927) = 48 and also period(1/7293) = 48.

Maple

with(numtheory): nn:=8000:for n from 3 to nn do: s:=0:l:=length(n):for q from 0 to l-1 do:x:=iquo(n, 10^q):y:=irem(x, 10):s:=s+y*10^(l-1-q): od: indic1:=0:for p from 1 to nn do:if irem(10^p, n) = 1 and gcd(n, 5) = 1 and indic1=0 then pp:=p: indic1:=1:else fi:od: indic2:=0:for p from 1 to nn do:if irem(10^p, s) = 1 and gcd(s, 5) = 1 and indic2=0 then ppp:=p:indic2:=1:else fi:od: if pp=ppp and indic1=1 and indic2=1 then print(n):else fi:od:

Crossrefs

Cf. A004086, A045572, A002329.

Sequence in context: A191181 A046807 A333423 * A338712 A263926 A114788

Adjacent sequences: A178833 A178834 A178835 * A178837 A178838 A178839

Keyword

nonn,base

Author

Michel Lagneau, Jun 16 2010

Status

approved