{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e0343c5c-7355-4dab-82d6-66814b21df7e",
   "metadata": {},
   "source": [
    "📜 **Пример 1.**\n",
    "Дано действительное положительное число $b$. \n",
    "Найти первый член последовательности $a_1$, $a_2$, $a_3$,... образованной по закону:\n",
    "$$\n",
    "a_1 = 1, \\quad\n",
    "a_i = a_{i - 1} - \\dfrac{1}{\\sqrt{i - 1}}, \\quad\n",
    "i = 2, 3, 4,\\ldots,\n",
    "$$\n",
    "больший, чем $b$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8c7bde8f-4d75-4cfe-be28-ae642550503c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      " 2.5\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   1     1.0000     True\n",
      "   2     2.0000     True\n",
      "   3     2.7071    False\n",
      "a[3] = 2.7071\n"
     ]
    }
   ],
   "source": [
    "# 1 вариант оформления трассы\n",
    "\n",
    "from math import sqrt\n",
    "\n",
    "b = float(input())\n",
    "\n",
    "i = 1\n",
    "a = 1\n",
    "print('%4d %10.4f %8s' %(i, a, a <= b))\n",
    "while a <= b:\n",
    "    i = i + 1\n",
    "    a = a + 1 / sqrt(i - 1)\n",
    "    print('%4d %10.4f %8s' %(i, a, a <= b))\n",
    " \n",
    "print('a[%d] = %6.4f' %(i, a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f56b0ccb-985a-4a25-aa4f-4e8eafbc233e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      " 2.5\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   1     1.0000     True\n",
      "   2     2.0000     True\n",
      "   3     2.7071    False\n",
      "a[3] = 2.7071\n"
     ]
    }
   ],
   "source": [
    "# 2 вариант оформления трассы\n",
    "\n",
    "from math import sqrt\n",
    "\n",
    "b = float(input())\n",
    "\n",
    "i = 1\n",
    "a = 1\n",
    "while a <= b:\n",
    "    print('%4d %10.4f %8s' %(i, a, a <= b))\n",
    "    i = i + 1\n",
    "    a = a + 1 / sqrt(i - 1)\n",
    "print('%4d %10.4f %8s' %(i, a, a <= b))\n",
    " \n",
    "print('a[%d] = %6.4f' %(i, a))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b286be2-fde0-411d-bf18-e96ab7bd8ec9",
   "metadata": {},
   "source": [
    "&#128220; **Пример 2.**\n",
    "Дано натуральное число $n$. \n",
    "Проверить, является ли это число правильной записью 8-ричного числа."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "bd3166f1-940d-4603-81f1-e6875375a9b5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      " 123064203\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   123064203     True\n",
      "    12306420     True\n",
      "     1230642     True\n",
      "      123064     True\n",
      "       12306     True\n",
      "        1230     True\n",
      "         123     True\n",
      "          12     True\n",
      "           1     True\n",
      "           0    False\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "n = int(input())\n",
    "\n",
    "m = n\n",
    "print('%12d %8s' %(m, m != 0 and m % 10 < 8))\n",
    "while m != 0 and m % 10 < 8:\n",
    "    m = m // 10\n",
    "    print('%12d %8s' %(m, m != 0 and m % 10 < 8))\n",
    "\n",
    "print(m == 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "8fea727d-3892-4031-b9d4-e85e87446dcb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      " 1200090034\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  1200090034     True     True     True\n",
      "   120009003     True     True     True\n",
      "    12000900     True     True     True\n",
      "     1200090     True     True     True\n",
      "      120009     True    False    False\n",
      "False\n"
     ]
    }
   ],
   "source": [
    "n = int(input())\n",
    "\n",
    "m = n\n",
    "print('%12d %8s %8s %8s' %(m, m != 0, m % 10 < 8, m != 0 and m % 10 < 8))\n",
    "while m != 0 and m % 10 < 8:\n",
    "    m = m // 10\n",
    "    print('%12d %8s %8s %8s' %(m, m != 0, m % 10 < 8, m != 0 and m % 10 < 8))\n",
    "\n",
    "print(m == 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66fdfe78-bc39-4ff9-ad28-779f8f36770c",
   "metadata": {},
   "source": [
    "&#128220; **Пример 3.**\n",
    "Дана последовательность ненулевых целых чисел.\n",
    "Количество элементов последовательности заранее неизвестно.\n",
    "Найти максимальный кратный 5 элемент последовательности."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2bef2776-2b29-4887-9e45-4e87ab459017",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = int(input())\n",
    "flag = True  #  нет макс элемента кратного 5\n",
    "while a != 0:\n",
    "    if abs(a) % 5 == 0:\n",
    "        if flag:\n",
    "            maxi = a\n",
    "            flag = False\n",
    "        else:  # макс хотя один в посл-ти есть\n",
    "            if a > maxi:\n",
    "                maxi = a\n",
    "    a = int(input())\n",
    "\n",
    "if flag:\n",
    "    print('нет чисел кратных 5')\n",
    "else:\n",
    "    print(maxi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "efd25efa-fd99-459c-8159-0a70061116ab",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}