move notebooks to subdir

notebooks/problem0016.ipynb

@@ -0,0 +1,68 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "78b44de2",
+   "metadata": {},
+   "source": [
+    "# [Power Digit Sum](https://projecteuler.net/problem=16)\n",
+    "\n",
+    "Since Python/SageMath support integers of arbitrary size, this problem is pretty straightforward. Just compute $2^{1000}$ directly and sum the digits up."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "d3a790fe",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1366\n"
+     ]
+    }
+   ],
+   "source": [
+    "n = 2 ^ 1000\n",
+    "total = 0\n",
+    "while n != 0:\n",
+    "    total += n % 10\n",
+    "    n //= 10\n",
+    "\n",
+    "print(total)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "60ba69ac",
+   "metadata": {},
+   "source": [
+    "## Relevant sequences\n",
+    "* Sums of digits of $2^n$: [A001370](https://oeis.org/A001370)"
+   ]
+  }
+ ],
+ "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
+}