%I #17 Aug 23 2023 08:35:21
%S 40,290,600,790,1350,1400,4580,4590,4640,4740,4750,9080,9480,9570,
%T 9600,11000,11020,11080,11160,11210,11240,11290,11310,11570,11590,
%U 11720,11780,11800,13870,13880,13990,14060,14250,14290,14310,14320,14340,14590,14760,15920,16390
%N Consider the sequence b(k) such that b(k) and sigma(b(k)) end with the same digit in base 10. Sequence gives values of b(k) such that b(k)/k = 10.
%C Conjecture: lim n -> infinity b(k)/k = 10.
%H David A. Corneth, <a href="/A065255/b065255.txt">Table of n, a(n) for n = 1..249</a> (terms <= 10^9)
%e b(k) begins 1,14,34,40,44,74,78,81,84 hence b(4)=40 and 40/4=10 so 40 is in the sequence.
%o (PARI) upto(n) = {my(b = List(), res = List(), t = 0); forfactored(i = 1, n, s = sigma(i[2]); if((s - i[1])%10 == 0, t++; if(10*t == i[1], listput(res, i[1])))); res} \\ _David A. Corneth_, Aug 23 2023
%Y Cf. A072566 (b).
%K base,nonn
%O 1,1
%A _Benoit Cloitre_, Aug 06 2002
%E Name corrected by _Sean A. Irvine_, Aug 23 2023
%E More terms from _David A. Corneth_, Aug 23 2023