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

1,3

Comments

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

Links

Table of n, a(n) for n=1..15.

Formula

a(n) < A052268(n).

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

Prog

(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

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).

Sequence in context: A306290 A075469 A028032 * A025986 A028027 A268764

Adjacent sequences: A348052 A348053 A348054 * A348056 A348057 A348058

Keyword

nonn,base,hard,more

Author

Stefano Spezia, Sep 26 2021

Extensions

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

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

Status

approved