Evan Gillard - cp's OEIS frontend

User: Evan Gillard

Evan Gillard has authored 1 sequences.

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

Evan Gillard, Jun 23 2023

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

			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.

Supersequence of A052224.

Cf. A342804, A357272.

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

cp's OEIS Frontend

User: Evan Gillard

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.

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