A347749 Number of positive integers with n digits and final digit 6 that are equal to the product of two integers ending with the same digit.

0, 4, 33, 352, 3597, 36781, 374071, 3790993, 38326689, 386782889

Offset

1,2

Comments

a(n) is the number of n-digit numbers in A347747.

Links

Table of n, a(n) for n=1..10.

Formula

a(n) < A052268(n).

a(n) = A337856(n) + A347255(n) - A347748(n).

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

Mathematica

Table[{lo, hi}={10^(n-1), 10^n}; Length@Select[Union[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<#<hi&], {n, 8}]

Prog

(Python)
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

Crossrefs

Cf. A017341, A052268, A324297, A337856, A347253, A347255, A347747, A347748.

Sequence in context: A093185 A198006 A339654 * A362604 A075132 A379172

Adjacent sequences: A347746 A347747 A347748 * A347750 A347751 A347752

Keyword

nonn,base,hard,more

Author

Stefano Spezia, Sep 12 2021

Extensions

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

Status

approved