Project Euler

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# [[Problem 36]]

## Double-base Palindromes

The decimal number, $585 = 1001001001_2$ (binary), is palindromic in both bases.

Find the sum of all numbers, less than one million, which are palindromic in base $10$ and base $2$.

(Please note that the palindromic number, in either base, may not include leading zeros.)

## 二種類の基数による回文数

$585 = 1001001001_2$ (2進) は10進でも2進でも回文数である.

100万未満で10進でも2進でも回文数になるような数の総和を求めよ.

(注: 先頭に0を含めて回文にすることは許されない.)

```scheme

(import (scheme base)

        (gauche base)

        (scheme flonum))

(define (number-of-digit n base)

  (assume (exact-integer? n))

  (assume (<= 0 n))

  (assume (or (= base 2)

              (= base 10)))

  (if (zero? n)

    1

    (+ (floor->exact

         ((if (= base 2)

            fllog2

            fllog10)

          n))

       1)))

(define (palindrome? n base)

  (assume (exact-integer? n))

  (assume (<= 0 n))

  (assume (or (= base 2)

              (= base 10)))

  (let* ([dn (number-of-digit n base)]

         [loop-count (div dn 2)])

    (let loop ([index 0])

      (cond

        [(<= loop-count index) #t]

        [(= (div (mod n (expt base (+ 1 index)))

                 (expt base index))

            (div (mod n (expt base (- dn index)))

                 (expt base (- dn 1 index))))

         (loop (+ index 1))]

        [else #f]))))

(define answer-36

  (apply + 

         (filter (cut palindrome? <> 2)

                 (filter (cut palindrome? <> 10)

                         (iota 100_0000)))))

(format #t "36: ~d~%" answer-36)

```