add problem 40

notebooks/problem0040.ipynb

@@ -0,0 +1,70 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "42c30745",
+   "metadata": {},
+   "source": [
+    "# [Champernowne's Constant](https://projecteuler.net/problem=40)\n",
+    "\n",
+    "This is certainly not the fastest or most clever solution for calculating digits of [Champernowne's constant](https://en.wikipedia.org/wiki/Champernowne_constant), but it's fast enough, and pretty comprehensible.\n",
+    "\n",
+    "Since there are so many strings to concatenate, for performance it is helpful to use the [`str.join` method](https://docs.python.org/3/library/stdtypes.html#str.join)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "deed40a4",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "210"
+      ]
+     },
+     "execution_count": 1,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "from itertools import count\n",
+    "\n",
+    "c = '.' + ''.join(str(k) for k in range(1, 1_000_001))\n",
+    "prod(int(c[i]) for i in (1, 10, 100, 1000, 10000, 100000, 1000000))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "59074921",
+   "metadata": {},
+   "source": [
+    "## Relevant sequences\n",
+    "* Digits of Champernowne's constant: [A033307](https://oeis.org/A033307)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "SageMath 9.5",
+   "language": "sage",
+   "name": "sagemath"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}