cp's OEIS Frontend

A056055 Integers k > 1 such that the decimal expansion of 1/k contains k as a string. (If the decimal expansion terminates, trailing zeros do not count.)

%I A056055 #19 Dec 02 2022 19:46:05
%S A056055 3,6,7,14,17,28,58,59,83,86,87,89,97,118,167,197,228,281,313,316,339,
%T A056055 367,379,383,456,458,469,529,541,543,569,577,587,593,607,618,626,629,
%U A056055 647,669,673,677,678,683,687,701,709,719,722,727,729,767,771,772,778
%N A056055 Integers k > 1 such that the decimal expansion of 1/k contains k as a string. (If the decimal expansion terminates, trailing zeros do not count.)
%C A056055 The sequence is probably infinite, since long-period primes (cf. A006883) especially with high first digit are likely candidates, but is there a proof? Does any k with finite expansion of 1/k (i.e., k = 2^j * 5^m) occur?
%H A056055 Nicolas Bělohoubek, <a href="/A056055/b056055.txt">Table of n, a(n) for n = 1..900</a>
%H A056055 <a href="/index/1#1overn">Index entries for sequences related to decimal expansion of 1/n</a>
%e A056055 118 is a term since 1/118 = 0.00847457627118... contains "118".
%e A056055 100 is not a term because 1/100 = 0.01 does not contain "100" (0.0100 does not count).
%K A056055 nonn,base
%O A056055 1,1
%A A056055 Ulrich Schimke (ulrschimke(AT)aol.com)