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

1,2

Comments

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

Links

Table of n, a(n) for n=1..14.

Formula

a(n) < A052268(n).

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

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<#<hi&], {n, 7}] (* Giorgos Kalogeropoulos, Aug 16 2021 *)

Prog

(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

Crossrefs

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

Sequence in context: A036942 A183960 A338717 * A336242 A054596 A155667

Adjacent sequences: A346949 A346950 A346951 * A346953 A346954 A346955

Keyword

nonn,base,hard,more

Author

Stefano Spezia, Aug 08 2021

Extensions

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

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

Status

approved