A347749 -id:A347749 - cp's OEIS frontend

A347747 Positive integers with final digit 6 that are equal to the product of two integers ending with the same digit.

16, 36, 56, 96, 136, 156, 176, 196, 216, 256, 276, 296, 336, 376, 396, 416, 456, 476, 496, 516, 536, 576, 616, 636, 656, 676, 696, 736, 756, 776, 816, 856, 876, 896, 936, 976, 996, 1016, 1036, 1056, 1096, 1116, 1136, 1156, 1176, 1196, 1216, 1236, 1256, 1296, 1316

Offset: 1

Stefano Spezia, Sep 12 2021

Union of A324297 and A347253.

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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

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

isok(m) = if ((m % 10) == 6, fordiv(m, d, if ((d % 10) == (m/d % 10), return(1)))); \\ Michel Marcus, Oct 06 2021

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)))
print(aupto(1317)) # Michael S. Branicky, Sep 12 2021

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

A347748 Number of positive integers with n digits that are equal both to the product of two integers ending with 4 and to that of two integers ending with 6.

Original entry on oeis.org

0, 1, 12, 159, 1859, 20704, 223525, 2370684, 24842265, 258128126, 2665475963

Offset: 1

Stefano Spezia, Sep 12 2021

a(n) is the number of n-digit numbers in A347746.

Cf. A017341, A052268, A324297, A337856, A347253, A347255, A347746, A347749.

Table[{lo, hi}={10^(n-1), 10^n}; Length@Select[Intersection[Union@Flatten@Table[a*b, {a, 4, Floor[hi/4], 10}, {b, a, Floor[hi/a], 10}],Union@Flatten@Table[a*b, {a, 6, Floor[hi/6], 10}, {b, a, Floor[hi/a], 10}]], lo<#

def a(n):
  lo, hi = 10**(n-1), 10**n
  return len(set(a*b for a in range(4, hi//4+1, 10) for b in range(a, hi//a+1, 10) if lo <= a*b < hi) & set(a*b for a in range(6, hi//6+1, 10) for b in range(a, hi//a+1, 10) if lo <= a*b < hi))
print([a(n) for n in range(1, 9)]) # Michael S. Branicky, Oct 06 2021

a(n) < A052268(n).
a(n) = A337856(n) + A347255(n) - A347749(n).
Conjecture: lim_{n->infinity} a(n)/a(n-1) = 10.

a(9)-a(10) from Michael S. Branicky, Oct 06 2021

a(11) from Frank A. Stevenson, Jan 06 2024

cp's OEIS Frontend

A347747 Positive integers with final digit 6 that are equal to the product of two integers ending with the same digit.

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