FYI, Project Euler problems 4, 36, 125, 486 involve
palindromic numbers.
They're publicly available at
https://projecteuler.net/archives
I think the earlier ones are quite straightforward.
125 concerns palindromes that are the sums of consecutive
non-zero squares, such as 595 = +/*: 7 8 9 10 11 12 , and
is perhaps quite interesting. The problem is to sum all such
palindromes < 1e8.
486 has only been solved by 132 punters in the year since
it was first posted. As usual, the difficulty lies in obtaining
a solution for the given extreme problem size. It doesn't
really concern palindromic numbers, though, since they're
boolean, or members of a two-letter alphabet if you wish
to regard them as such.
"Palindrome-containing strings
Problem 486
Let F_5 (n) be the number of stringsssuch that:
* sconsists only of '0's and '1's,
* shas length at mostn, and
* scontains a palindromic substring of length at least 5.
For example, F_5 (4) = 0, F_5 (5) = 8, F_5 (6) = 42 and F_5 (11) = 3844.
Let D(L) be the number of integersnsuch that 5 ≤ n ≤ Land F_5 (n) is
divisible by 87654321.
For example, D(10^7 ) = 0 and D(5·10^9 ) = 51.
Find D(10^18 ).
"
My solution in J takes far too long, ~ 3 minutes, compared with
the stated Euler target of less than a minute.
I have a Pari GP solution, too, but can't remember how to get it
to reproduce the result!
Mike
On 15/10/2015 18:02, Kip Murray wrote:
Please read below. Forwarding is the only way I can get my awkward mailer
to send you a message with copied material! --Kip Murray
---------- Forwarded message ---------
From: km <[email protected]>
Date: Thu, Oct 15, 2015 at 11:44 AM
Subject: Finding prime palindromes
To: Kip Murray <[email protected]>
A prime palindrome is a prime which is unchanged when its decimal digits
are reversed. Write verb find below.
p: i.40 NB. first 41 primes
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101
103 107 109 113 127 131 137 139 149 151 157 163 167 173
find i.40 NB. palindromes among the first 41 primes
2 3 5 7 11 101 131 151
--Kip Murray
Sent from my iPad
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