|
%I #44 Jun 11 2022 06:32:14
%S 1,13,145,153,1825,15789,16666,21583,216666,2416666,28428571,
%T 265833333,3194444444,3333333333,9111111111,35333333333,3166666666666,
%U 3819444444444,26666666666666,34166666666666,527857142857142,3944444444444444,6135714285714285,615833333333333333
%N Numbers k such that the decimal expansion of the sum of the reciprocals of the digits of k starts with the digits of k in the same order.
%C The sequence is infinite because all numbers of the form 10^(10^n-6) + 6*(10^(10^n-6)-1)/9, (n>0) are terms.
%C All terms are zeroless since 1/0 is undefined.
%C If n gives a sum < 1 then that sum is taken as 0.xyz.. but n does not start with 0, so not a term.
%H Kevin Ryde, <a href="/A354466/b354466.txt">Table of n, a(n) for n = 1..382</a>
%H Michael S. Branicky, <a href="/A354466/a354466_1.py.txt">Python program</a>
%H Kevin Ryde, <a href="/A354466/a354466.gp.txt">PARI/GP Code</a>
%e 28428571 is a term because 1/2 + 1/8 + 1/4 + 1/2 + 1/8 + 1/5 + 1/7 + 1/1 = 2.8428571...
%e 825 is not a term since 1/8 + 1/2 + 1/5 = 0.825.
%t Do[If[FreeQ[IntegerDigits[n], 0]&&Floor[Total[1/IntegerDigits[n]]*10^(IntegerLength[n]-IntegerLength[Floor[Total[1/IntegerDigits[n]]]])]==n&&Floor[Total[1/IntegerDigits[n]]]>0, Print[n]], {n, 1, 216666}]
%o (Python) See links.
%o (PARI) See links.
%Y Cf. A009994, A034708, A337904.
%K nonn,base
%O 1,2
%A _Metin Sariyar_, Jun 01 2022
%E a(12)-a(24) from _Michael S. Branicky_, Jun 03 2022
| 