A348055 Number of positive integers with n digits that are the product of two integers ending with 7.

0, 1, 20, 255, 3064, 34743, 380939, 4089499, 43282317, 453472867, 4715695283, 48760330737, 501941505404, 5148657883067, 52659616820819

Offset: 1

Author

Stefano Spezia, Sep 26 2021

Keywords

• nonn
• base
• hard
• more

Comments

a(n) is the number of n-digit numbers in A348054.

Crossrefs

Cf. A017377, A052268, A348054.

Cf. A346509 (ending with 1), A346629 (ending with 2), A346952 (ending with 3), A347255 (ending with 4), A337855 (ending with 5), A337856 (ending with 6), A348549 (ending with 8).

Programs

Python

def a(n):
  lo, hi = 10**(n-1), 10**n
  return len(set(a*b for a in range(7, hi//7+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, Sep 26 2021

Formula

a(n) < A052268(n).

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

Extensions

a(9)-a(11) from Michael S. Branicky, Sep 26 2021

a(12)-a(15) from Martin Ehrenstein, Oct 25 2021