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

1,1

Links

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

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

Example

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

Prog

(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

Crossrefs

Sequence in context: A160861 A302575 A302801 * A078273 A345391 A065571

Adjacent sequences: A067039 A067040 A067041 * A067043 A067044 A067045

Keyword

base,nonn,easy

Author

Amarnath Murthy, Dec 29 2001

Extensions

Corrected by David Wasserman, Jan 16 2002

More terms from Sascha Kurz, Mar 23 2002

Status

approved