A346952 Number of positive integers with n digits that are the product of two integers ending with 3.

1, 3, 37, 398, 4303, 45765, 480740, 5005328, 51770770, 532790460, 5461696481, 55814395421, 568944166801, 5787517297675

Offset: 1

Author

Stefano Spezia, Aug 08 2021

Keywords

• nonn
• base
• hard
• more

Comments

a(n) is the number of n-digit numbers in A346950.

Crossrefs

Cf. A017377, A052268, A346509 (ending with 1), A337855 (ending with 5), A337856 (ending with 6), A346950.

Programs

Mathematica

Table[{lo,hi}={10^(n-1),10^n};Length@Select[Union@Flatten@Table[a*b,{a,3,Floor[hi/3],10},{b,a,Floor[hi/a],10}],lo<#Giorgos Kalogeropoulos, Aug 16 2021 *)

Python

def a(n):
  lo, hi = 10**(n-1), 10**n
  return len(set(a*b for a in range(3, hi//3+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, Aug 09 2021

Formula

a(n) < A052268(n).

Conjecture: Lim_{n->infinity} a(n)/a(n-1) = 10.

Extensions

a(6)-a(11) from Michael S. Branicky, Aug 09 2021

a(12)-a(14) from Martin Ehrenstein, Aug 22 2021