A324297 - OEIS

%I #37 Aug 21 2021 15:45:56

%S 36,96,156,216,256,276,336,396,416,456,516,576,636,676,696,736,756,

%T 816,876,896,936,996,1056,1116,1176,1196,1216,1236,1296,1356,1376,

%U 1416,1456,1476,1536,1596,1656,1696,1716,1776,1836,1856,1896,1956,1976,2016,2076,2116

%N Positive integers k that are the product of two integers ending with 6.

%C All the terms end with 6 (A017341).

%H Stefano Spezia, <a href="/A324297/b324297.txt">Table of n, a(n) for n = 1..10000</a>

%F Conjecture: Lim_{n->infinity} a(n)/a(n-1) = 1.

%F The conjecture is true since it can be proved that a(n) = (sqrt(a(n-1)) + g(n-1))^2 where [g(n): n > 1] is a bounded sequence of positive real numbers. - _Stefano Spezia_, Aug 18 2021

%e 36 = 6*6, 96 = 6*16, 216 = 6*36, 256 = 16*16, 276 = 6*46, ...

%t a={}; For[n=0,n<=250,n++,For[k=0,k<=n,k++,If[Mod[10*n+6,10*k+6]==0 && Mod[(10*n+6)/(10*k+6),10]==6 && 10*n+6>Max[a],AppendTo[a,10*n+6]]]]; a

%o (PARI) isok6(n) = (n%10) == 6; \\ A017341

%o isok(n) = {if (isok6(n), my(d=divisors(n)); fordiv(n, d, if (isok6(d) && isok6(n/d), return(1)));); return (0);} \\ _Michel Marcus_, Apr 14 2019

%o (Python)

%o def aupto(lim): return sorted(set(a*b for a in range(6, lim//6+1, 10) for b in range(a, lim//a+1, 10)))

%o print(aupto(2117)) # _Michael S. Branicky_, Aug 18 2021

%Y Cf. A000400, A017341 (supersequence), A324298, A053742 (ending with 5).

%K nonn,base

%O 1,1

%A _Stefano Spezia_, Mar 16 2019