Distinct palindromes within decimal numbers
Find all distinct palindromes contained as substrings in decimal representation of n. Note that for the purpose of the initial function, a single digit will be considered a palindrome.
Distinct palindromes within decimal numbers is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
- Task
- Find all the palindromes including single digits in the integers from 100 to 125, inclusive.
- Determine which if any of the following decimal integers contain palindromes of 2 digits or more:
9, 169, 12769, 1238769, 123498769, 12346098769, 1234572098769, 123456832098769, 12345679432098769, 1234567905432098769, 123456790165432098769, 83071934127905179083, 1320267947849490361205695
- Also see
-
- OEIS entry: A262188 (Task 1).
- OEIS entry: A151997 (Task 2).
Related tasks
Palindrome_detection
Longest_palindromic_substrings
N_1's_followed_by_a_3
Julia
<lang julia>function allpalindromes(a::Vector{T}) where T
pals = Vector{Vector{T}}([[x] for x in a]) len = length(a) len < 2 && return pals a == reverse(a) && push!(pals, a) len == 2 && return pals for i in 2:len left = a[1:i] left == reverse(left) && push!(pals, left) end return unique(vcat(pals, allpalindromes(a[2:end])))
end
println("Number Palindromes") for n in 100:125
println(" ", rpad(n, 7), sort(allpalindromes(digits(n))))
end
palindrome2plusfree(n) = (a = allpalindromes(digits(n)); all(x -> length(x) == 1, a))
println("\nNumber Has no > 2 digit palindromes") for n in [9, 169, 12769, 1238769, 123498769, 12346098769, 1234572098769, 123456832098769,
12345679432098769, 1234567905432098769, 123456790165432098769, 83071934127905179083, 1320267947849490361205695] println(rpad(n, 26), palindrome2plusfree(n))
end
</lang>
- Output:
Number Palindromes 100 [[0], [0, 0], [1]] 101 [[0], [1], [1, 0, 1]] 102 [[0], [1], [2]] 103 [[0], [1], [3]] 104 [[0], [1], [4]] 105 [[0], [1], [5]] 106 [[0], [1], [6]] 107 [[0], [1], [7]] 108 [[0], [1], [8]] 109 [[0], [1], [9]] 110 [[0], [1], [1, 1]] 111 [[1], [1, 1], [1, 1, 1]] 112 [[1], [1, 1], [2]] 113 [[1], [1, 1], [3]] 114 [[1], [1, 1], [4]] 115 [[1], [1, 1], [5]] 116 [[1], [1, 1], [6]] 117 [[1], [1, 1], [7]] 118 [[1], [1, 1], [8]] 119 [[1], [1, 1], [9]] 120 [[0], [1], [2]] 121 [[1], [1, 2, 1], [2]] 122 [[1], [2], [2, 2]] 123 [[1], [2], [3]] 124 [[1], [2], [4]] 125 [[1], [2], [5]] Number Has no > 2 digit palindromes 9 true 169 true 12769 true 1238769 true 123498769 true 12346098769 true 1234572098769 true 123456832098769 true 12345679432098769 true 1234567905432098769 true 123456790165432098769 true 83071934127905179083 true 1320267947849490361205695 false