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

Author

Michel Lagneau, Jun 16 2010

Keywords

• nonn
• base

Comments

Non-palindromic numbers are included in this sequence :

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

Examples

			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.
		

Crossrefs

Cf. A004086, A045572, A002329.

Programs

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: