A347747 - OEIS

%I #14 Dec 27 2021 15:15:01

%S 16,36,56,96,136,156,176,196,216,256,276,296,336,376,396,416,456,476,

%T 496,516,536,576,616,636,656,676,696,736,756,776,816,856,876,896,936,

%U 976,996,1016,1036,1056,1096,1116,1136,1156,1176,1196,1216,1236,1256,1296,1316

%N Positive integers with final digit 6 that are equal to the product of two integers ending with the same digit.

%C Union of A324297 and A347253.

%H Harvey P. Dale, <a href="/A347747/b347747.txt">Table of n, a(n) for n = 1..1000</a>

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

%e 16 = 4*4, 36 = 6*6, 56 = 4*14, 96 = 4*24 = 6*16, 136 = 4*34, 156 = 6*26, ...

%t a={}; For[n=0, n<=150, n++, For[k=0, k<=n, k++, If[Mod[10*n+6, 10*k+4]==0 && Mod[(10*n+6)/(10*k+4), 10]==4 && 10*n+6>Max[a] || 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

%t tisdQ[n_]:=AnyTrue[{Mod[#,10],Mod[n/#,10]}&/@Divisors[n],#[[1]] == #[[2]]&]; Select[10 Range[150]+6,tisdQ] (* _Harvey P. Dale_, Dec 27 2021 *)

%o (Python)

%o def aupto(lim): return sorted(set(a*b for a in range(4, lim//4+1, 10) for b in range(a, lim//a+1, 10)) | set(a*b for a in range(6, lim//6+1, 10) for b in range(a, lim//a+1, 10)))

%o print(aupto(1317)) # _Michael S. Branicky_, Sep 12 2021

%o (PARI) isok(m) = if ((m % 10) == 6, fordiv(m, d, if ((d % 10) == (m/d % 10), return(1)))); \\ _Michel Marcus_, Oct 06 2021

%Y Cf. A017341 (supersequence), A324297, A347253, A347749.

%K nonn,base

%O 1,1

%A _Stefano Spezia_, Sep 12 2021