Distinct palindromes within decimal numbers
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.
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.
- 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