A363802 Numbers whose digits can be interposed with one or more of the arithmetic operators +, -, *, /, with no parentheses or concatenation, to yield 10 as the result.

19, 25, 28, 37, 46, 52, 55, 64, 73, 82, 91, 109, 118, 119, 125, 127, 128, 133, 136, 137, 145, 146, 152, 154, 155, 163, 164, 172, 173, 181, 182, 190, 191, 208, 215, 217, 218, 219, 224, 226, 229, 234, 235, 242, 244, 250, 251, 253, 262, 271, 274, 280, 281, 286, 291, 298, 307

Offset: 1

Author

Evan Gillard, Jun 23 2023

Keywords

• nonn
• base

Comments

This sequence is a variant of a "game" you can play using the numbers on train carriages (usually 4 digits in Australia's case), ignoring prefixed zeros, preventing re-ordering of the digits and allowing only addition, subtraction, multiplication and division.

No parentheses or concatenation are allowed and expressions follow operator precedence (*/) then (+-), and left to right within the same level of precedence: "2 + 3 * 2 / 6" is 2 + ((3*2)/6) = 2 + 1 = 3.

Infinite since A052224 is a subsequence. - Michael S. Branicky, Jun 24 2023

Examples

			1 + 9 = 2 + 8 = 1 * 9 + 1 = 2 * 9 - 8 = 10 so 19, 28, 191 and 298 are terms.
110 is not a term even though 1 * 10 = 10 since concatenation is disallowed.
		

Crossrefs

Supersequence of A052224.

Cf. A342804, A357272.

Programs

Python

from itertools import product
from fractions import Fraction
def is_A363802(n):
    s = [f"Fraction({d}, 1)" for d in str(n)]
    for ops in product("+-*/", repeat=len(s)-1):
        try: v = eval("".join(sum(zip(ops, s[1:]), (s[0],))))
        except: v = None
        if v == 10: return True
    return False
# Evan Gillard and Michael S. Branicky, Jun 23 2023