A178495 - OEIS

%I #11 Nov 16 2023 18:19:41

%S 1,11,41,81,111,187,231,451,567,891,1111,1197,1221,1539,1717,1881,

%T 2329,2877,3003,3591,3813,4551,4773,5643,6237,6327,7371,8991,9399,

%U 9449,10773,11111,11583,13167,13651,15561,16863,17589,23331,24453,27371,39501

%N Numbers k whose sum of digits equals the period of 1/k.

%D J. W. L. Glaisher, On circulating decimals, Proc. Camb. Phil. Soc., 3 (1878), pp. 185-206.

%D D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, pp. 7-12.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DecimalExpansion.html">Decimal Expansion</a>.

%F {k: A084680(k) = A007953(k)}. - _R. J. Mathar_, Jun 07 2010

%e 11 is in the sequence because 1 + 1 = 2 and 1/11 = 0.09 09 09... with period 2.

%e 41 is in the sequence because 4 + 1 = 5 and 1/41 = 0.02439 02439 ... with period 5.

%p with(numtheory): nn:= 2343: T:=array(1..nn): U:=array(1..nn): X:=array(1..nn): Y:=array(1..nn):k:=1:for n from 2 to 999999 do:for p from 1 to 55 while(irem(10^p,n)<>1 or gcd(n,10)<> 1) do: od: if irem(10^p,n) = 1 and gcd(n,10) = 1 then T[k]:=n : U[k]:=p: k:=k+1:else fi:od: for n from 1 to nn do:p1:= T[n]: l:=length(p1):n0:=p1:s:=0:for m from 1 to l do:q:=n0:u:=irem(q,10):v:=iquo(q,10):n0:=v :s:=s+u:od: X[n]:=s: od: for n from 1 to nn do:if X[n]= U[n] then printf(`%d, `, T[n]):else fi:od:

%Y Cf. A002329, A007953, A084680.

%K nonn,base

%O 1,2

%A _Michel Lagneau_, May 28 2010