Date: Wed, 11 Feb 2009 02:56:36 -0800 (PST)
From: Farideh Firoozbakht <mymontain(AT)yahoo.com>

Comments on A098282

Out of the first 1000 natural numbers there are only the following 62 numbers
for which Mma can't compute a(n).
 
A={40,52,87,106,116,164,173,189,192,204,210,239,240,259,276,284,
 342,345,372,375,377,385,392,412,436,449,480,501,519,560,577 ,
 610,622,641,642,644,675,682,684,728,734,737,759,764,801,816 ,
 831,834,854,861,874,905,908,922,925,940,958,966,971,975,985 ,990}
 
For the remaining n the values of {n,a(n)} are:
 
{1,1}, {2,2}, {3,3}, {4,6}, {5,4}, {6,31}, {7,7}, {8,55}, {9,4},{10,33}, {11,5}, {12,30}, {13,32},
{14,1}, {15,4}, {16,19}, {17,8},{18,112}, {19,56}, {20,16}, {21, 27}, {22,4}, {23,4}, {24,26},
{25,2}, {26,20}, {27,223}, {28,102}, {29, 34}, {30, 14}, {31, 6}, {32,162}, {33,2}, {34,9}, {35,10},
{36,75}, {37,31}, {38,113}, {39,21}, {41,33}, {42,20}, {43,2}, {44,23}, {45,30}, {46,57}, {47,5},
{48,28}, {49,24}, {50,30}, {51,224}, {53,20}, {54,295}, {55,11}, {56,85}, {57,103}, {58,140},
{59,9}, {60,71}, {61,113}, {62,55}, {63,34}, {64,110}, {65,76}, {66,49},{67,57}, {68,110},
{69,35}, {70,8}, {71,17}, {72,165}, {73,28}, {74,30},{75,226}, {76,111}, {77,31}, {78, 153},
{79,5}, {80,77}, {81,112}, {82,16}, {83,5}, {84,144}, {85,32}, {86,102}, {88,69}, {89,27},
{90,277}, {91,58},{92,7}, {93,7}, {94,23}, {95,114}, {96,62}, {97,3}, {98,99}, {99,94}, {100,115},
 {101,21}, {102,8}, {103,224}, {104,53}, {105,28}, {107,103},{108,23}, {109,35}, {110,139},
{111,54}, {112,29}, {113,15}, {114,101}, {115,22},{117,109}, {118,110}, {119,6}, {120,11},
{121,12}, {122,111}, {123,13},{124,19}, {125,48}, {126,152}, {127,7}, {128,100}, {129,102},
{130,107},{131,163}, {132,182}, {133,29}, {134,7}, {135,138}, {136,106}, {137,3}, {138,103},
{139,10}, {140,163}, {141,6}, {142,12}, {143,86}, {144,98},{145,35}, {146,13}, {147,77},
{148,26}, {149,11}, {150,94}, {151,76},{152,76}, {153,26}, {154,36}, {155,112}, {156,16},
{157,32},{158,112}, {159,111}, {160,220}, {161,25}, {162,24}, {163,114}, {165,112}, {166,14},
{167,22}, {168,361}, {169,50}, {170,4}, {171,157}, {172,85}, {174,10}, {175,12}, {176,175},
{177,228}, {178,20}, {179,34}, {180,75}, {181,21}, {182,14}, {183,104}, {184,32}, {185,13},
{186, 92}, {187, 104}, {188,69}, {190,104}, {191,3}, {193,24}, {194,49}, {195,107}, {196,64},
{197,31}, {198,38}, {199,58},{200,275}, {201,60}, {202,153}, {203,116}, { 205,78},
{206,8}, {207,32},{208,78}, {209,141}, {211,6}, {212,53}, {213,12}, {214, 101}, {215,5},
{216,110}, {217,227}, {218,103}, {219,59}, {220,11}, {221,58}, {222,222}, {223,29}, {224,33},
{225, 93}, {226,108}, {227,25}, {228,156}, {229,31}, {230,11}, {231,31}, {232, 21}, {233,225},
{234,27}, {235,111}, {236,106}, {237,223}, {238,78}, {241,21}, {242,113}, {243,144}, {244,76},
{245, 30}, {246,40}, {247,111}, {248,162}, {249,30}, {250, 86}, {251,296}, {252,88}, {253,10},
{254,164}, {255,224}, {256,173}, {257,12}, {258, 20}, {260,72}, {261,62}, {262,183}, {263,86},
{264,131}, {265,76}, {266,27}, {267,34}, {268,32}, {269, 104}, {270,26}, {271,141}, {272,33},
{273,41}, {274,30}, {275,121}, {277,10}, {278,8}, {279,217}, {280,25}, {281,72}, {282,32},
{283,114}, {285, 79}, {286,17}, {287,30}, {288,98}, {289,32}, {290,139}, {291,94}, {292,126},
{293, 56}, {294,56}, {295,51}, {296,28}, {297,115}, {298,139}, {299,36}, {300,129}, {301,63},
{302,107}, {303,109}, {304,13}, {305,39}, {306,27}, {307,35}, {308,76}, {309,26}, {310,34},
{311,111}, {312,12}, {313,77}, {314,4}, {315,110}, {316,75}, {317,50}, {318,38}, {319,119},
{320,67}, {321,157}, {322,12}, {323,154}, {324,117}, {325,49}, {326,104}, {327,32}, {328,77},
{329,156}, {330,36}, {331,58}, {332,71}, {333,47}, {334,11}, {335,120}, {336,48}, {337,111},
{338,15}, {339,12}, {340,123}, {341,19}, {343,51}, {344,29}, {346,164}, {347,36}, {348,67},
{349,9}, {350,74}, {351,130}, {352,266}, {353,18}, {354,60}, {355,68},{356,144}, {357,112},
{358,7}, {359,166}, {360,86}, {361,70}, {362,13}, {363,225}, {364,232}, {365,158}, {366,274},
{367,29}, {368,34}, {369,38}, {370,68}, {371,151}, {373,31}, {374,33}, {376,175}, {378,292},
{379,227}, {380,52}, {381,32}, {382,87}, {383,112}, {384,91}, {386,99}, {387,232}, {388,182},
{389,32}, {390, 18}, {391, 6}, {393,22}, {394,36}, {395,13}, {396,54}, {397,154}, {398,14},
{399,163}, {400,24}, {401,6}, {402,26}, {403,183}, {404,16}, {405,159}, {406,130}, {407,125},
{408,22}, {409,78}, {410,115}, {411,226}, {413,29}, {414,62}, {415,155}, {416,150}, {417,28},
{418,113}, {419,113}, {420, 206}, {421,17}, {422,78}, {423,101}, {424,78}, {425,112},
{426,461}, {427,114}, {428,156}, {429,174}, {430,40}, {431,6}, {432,219}, {433,145}, {434,13},
{435,247}, {437,28}, {438,129}, {439,33}, {440,90}, {441,107}, {442,23}, {443,103}, {444,50},
{445,118}, {446,27}, {447,112}, {448,127}, {450,24}, {451,254}, {452,35}, {453,107}, {454,12},
{455,165}, {456,231}, {457,70}, {458,95}, {459,74}, {460,103}, {461,28}, {462,108}, {463,278},
{464,265}, {465,31}, {466,77}, {467,59}, {468,221}, {469,114}, {470,146}, {471,224}, {472,33},
{473,114}, {474,295}, {475,16}, {476,27}, {477,54}, {478,77}, {479,8}, {481,18}, {482,27},
{483,31}, {484,224}, {485,50}, {486,122}, {487,8}, {488,13}, {489,79}, {490,75}, {491,24},
{492,223}, {493,184}, {494,362}, {495,9}, {496,110}, {497,207}, {498,277}, {499,115},
{500,205}, {502,37}, {503,63}, {504,147}, {505,105}, {506,112}, {507,28}, {508,111}, {509,4},
{510,118}, {511,18}, {512,124}, {513,253}, {514,113}, {515,33}, {516,245}, {517,34}, {518,27},
{520,153}, {521,100}, {522,197}, {523,95}, {524,34}, {525,11}, {526,17}, {527,113}, {528,127},
{529,95}, {530,229}, {531,160}, {532,117}, {533,31}, {534,152}, {535,78}, {536,34}, {537,22},
{538,33}, {539,119}, {540,44}, {541,116}, {542,113}, {543,114}, {544,164}, {545,157},
{546,50}, {547,22}, {548,115}, {549,81}, {550,214}, {551,77}, {552,38}, {553,79}, {554,112},
{555,11}, {556,163}, {557,9}, {558,226}, {559,116}, {561,13}, {562,221}, {563,225}, {564,72},
{565,37}, {566,26}, {567,63}, {568,57}, {569,54}, {570,86}, {571,29}, {572,130}, {573,145},
{574,74}, {575,13}, {576,76}, {578,229}, {579,77}, {580,17}, {581,102}, {582,38}, {583,246},
{584,66}, {585,93}, {586,25}, {587,104}, {588,134}, {589,8}, {590,81}, {591,31}, {592,62},
{593,24}, {594,458}, {595,37}, {596,11}, {597,41}, {598,51}, {599,36}, {600,149}, {601,140},
{602,112}, {603,79}, {604,72}, {605,69}, {606,27}, {607,55}, {608,265}, {609,37}, {611,182},
{612,17}, {613,30}, {614,115}, {615,181}, {616,31}, {617,16}, {618,27}, {619,102}, {620,62},
{621,39}, {623,79}, {624,209}, {625,56}, {626,113}, {627,21}, {628,123}, {629,362}, {630,170},
{631,23}, {632,165}, {633,112}, {634,15},{635,59}, {636,158}, {637,28}, {638,61}, {639,359},
{640,86}, {643,110}, {645,51}, {646,21}, {647,111}, {648,137}, {649,35}, {650,60}, {651,9},
{652,52}, {653,7}, {654,62}, {655,72}, {656,220}, {657,60}, {658,72}, {659,12}, {660,147},
{661,13}, {662,23}, {663,35}, {664,11}, {665,68}, {666,30}, {667,77}, {668,103}, {669,163},
{670,7}, {671,28}, {672,247}, {673,112}, {674,362}, {676,114}, {677,14}, {678,130}, {679,113}
, {680,316}, {681,31}, {683,20}, {685,48}, {686,160}, {687,87}, {688,33}, {689,32}, {690,169},
{691,49}, {692,82}, {693,234}, {694,51}, {695,12}, {696,105}, {697,19}, {698,5}, {699,297},
{700,100}, {701,153}, {702,94}, {703,84}, {704,136},{705,20}, {706,158}, {707,462},
{708,235}, {709,8}, {710,183}, {711,112}, {712,361}, {713,18}, {714,4}, { 715,145}, {716,131},
{717,89}, {718,86}, {719,101}, {720,206}, {721,115}, {722,70}, {723,11}, {724,32},
{725,62}, {726,62}, {727,103}, {729,205}, {730,112}, {731,5}, {732,72}, {733,108}, {735,110},
{736,22}, {738,160}, {739,164}, {740,113}, {741,33}, {742,211}, {743,183}, {744,157},
{745,121}, {746,11}, {747,138}, {748, 211}, {749,157}, {750,156}, {751,30}, {752,266},
{753,165}, {754,90}, {755,49}, {756,145}, {757,8}, {758,13}, {760,41}, {761,139}, {762,155},
{763,175}, {765,73}, {766,176}, {767,17}, {768,58}, {769,107}, {770,114}, {771,225},
{772,64}, {773,4}, {774,32}, {775,74}, {776,131}, {777,149}, {778,229}, { 779,22}, {780,359},
{781,154}, {782,35}, {783,90}, {784,316}, {785,112}, {786,190}, {787,104}, {788,76},
{789,174}, {790,127}, {791,41}, {792,100}, {793,28}, {794,21}, {795,135}, {796,232},
{797,11}, {798, 158}, {799,146}, {800,74}, {802,35}, {803,101}, {804,33}, {805,10},
{806,161}, {807,13}, {808,12}, {809,164}, {810,76}, {811,7}, {812,83}, {813,21}, {814,123},
{815,16}, {817,124}, {818,76}, {819,160}, {820,87}, {821,13}, {822,94}, {823,87},
{824,22}, {825,8}, {826,364}, {827,99}, {828,185}, {829,36}, {830,179}, {832,125}, {833,113},
{835,13}, {836,57}, {837,182}, {838,22}, {839,14}, {840,231}, {841,27}, {842,15}, {843,73},
{844,27}, {845,275}, {846,225}, {847,166}, {848,150}, {849,63}, {850,105}, {851,68},
{852,80}, {853,78}, {855,112}, {856,231}, {857,27}, {858,317}, {859,12}, {860,71}, {862,105},
{863,95}, {864,238}, {865,124}, {866,33}, {867,11}, {868,172}, {869,198}, {870,259},
{871,103}, {872,38}, {873,115}, {875,71}, {876,238}, {877,77}, {878,14}, {879,184},
{880,237}, {881,77}, {882,119}, {883,27}, {884,12}, {885,61}, {886,93}, {887,37}, {888,242},
{889,7}, {890,13}, {891,68}, {892,117}, {893,17}, {894,36}, {895,20}, {896,20}, {897,105},
{898,105}, {899,34}, {900,33}, {901,132}, {902,34}, {903,104}, {904,112}, {906,18},
{907,113}, {909,130}, {910,76}, {911,17}, {912, 67}, {913,96}, {914,70}, {915,96}, {916,24},
{917,220}, {918,59}, {919,33}, {920, 59}, {921, 87}, {923,63}, {924,140}, {926,105}, {927,74},
{928,195}, {929,113}, {930,26}, {931,128}, {932,106}, {933,132}, {934,4}, {935,113},
{936,171}, {937,112}, {938,76}, {939,77}, {941,221}, {942,118}, {943,97}, {944,164},
{945,220}, {946,164}, {947,26}, {948,23}, {949,40}, {950,159}, {951,28}, {952,178},
{953,25}, {954,16}, {955,52}, {956, 90}, {957,73}, {959,146}, {960, 56}, {961,19}, {962,228},
{963,253}, {964,5}, {965,30}, {967,115}, {968,146}, {969,9}, {970,33}, {972,139}, {973,14},
{974,25}, {976,265}, {977,113}, {978,86}, {979,35}, {980,247}, {981,39}, {982,50}, {983,15},
{984,260}, {986,162}, {987,103}, {988,32}, {989,71}, {991,23}, {992,100}, {993,35},
{994,28}, {995,165}, {996,75}, {997,362}, {998,108}, {999,122}, {1000,99}
 
It's interesting that a(222)=222. 
 
The known fixed points of A098282 (a(n)=n) are: 1, 2, 3, 7, 222, ...
Presumably if n is in A then a(n)<>n.
 
Farideh