A067042 Numbers in which the product of digits in even positions = product of digits in odd positions.

11, 22, 33, 44, 55, 66, 77, 88, 99, 100, 111, 122, 133, 144, 155, 166, 177, 188, 199, 200, 221, 242, 263, 284, 300, 331, 362, 393, 400, 441, 482, 500, 551, 600, 661, 700, 771, 800, 881, 900, 991, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009

Offset: 1

Author

Amarnath Murthy, Dec 29 2001

Keywords

• base
• nonn
• easy

Examples

			2364 is a member as 2*6 = 3*4.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008593 (similar for sums).

Programs

Mathematica

Select[Range[1010], Product[Part[(digits=IntegerDigits[#]), 2i], {i, Floor[(len=IntegerLength[#])/2]}] == Product[Part[digits, 2i-1], {i,Ceiling[len/2]}] &] (* Stefano Spezia, Jan 05 2025 *)

Python

from math import prod
def ok(n):
    s = str(n)
    return s != '1' and prod(map(int, s[::2])) == prod(map(int, s[1::2]))
print([k for k in range(1010) if ok(k)]) # Michael S. Branicky, Nov 22 2021

Formula

Asymptotics: For any n, let f(n) be the number of entries in this sequence that are less than n. Then f(n)/n approaches 1 as n goes to infinity. This is because among numbers with a large number of digits, almost all have 0's in both odd positions and even positions. - David Wasserman, Jan 16 2002

Extensions

Corrected by David Wasserman, Jan 16 2002

More terms from Sascha Kurz, Mar 23 2002