cp's OEIS Frontend

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.

%I A363802 #47 Sep 02 2023 22:38:17
%S A363802 19,25,28,37,46,52,55,64,73,82,91,109,118,119,125,127,128,133,136,137,
%T A363802 145,146,152,154,155,163,164,172,173,181,182,190,191,208,215,217,218,
%U A363802 219,224,226,229,234,235,242,244,250,251,253,262,271,274,280,281,286,291,298,307
%N 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.
%C A363802 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.
%C A363802 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.
%C A363802 Infinite since A052224 is a subsequence. - _Michael S. Branicky_, Jun 24 2023
%e A363802 1 + 9 = 2 + 8 = 1 * 9 + 1 = 2 * 9 - 8 = 10 so 19, 28, 191 and 298 are terms.
%e A363802 110 is not a term even though 1 * 10 = 10 since concatenation is disallowed.
%o A363802 (Python)
%o A363802 from itertools import product
%o A363802 from fractions import Fraction
%o A363802 def is_A363802(n):
%o A363802     s = [f"Fraction({d}, 1)" for d in str(n)]
%o A363802     for ops in product("+-*/", repeat=len(s)-1):
%o A363802         try: v = eval("".join(sum(zip(ops, s[1:]), (s[0],))))
%o A363802         except: v = None
%o A363802         if v == 10: return True
%o A363802     return False
%o A363802 # _Evan Gillard_ and _Michael S. Branicky_, Jun 23 2023
%Y A363802 Supersequence of A052224.
%Y A363802 Cf. A342804, A357272.
%K A363802 nonn,base
%O A363802 1,1
%A A363802 _Evan Gillard_, Jun 23 2023