All x, such that there exists i > 1: f(x - i) + f(i) < f(x - 1) + 1 x = 21080618, i = 6, f(x - i) = 49, f(x - 1) = 54; found by CD_Eater (Igor) x = 63241604, i = 6, f(x - i) = 52, f(x - 1) = 57 x = 67139098, i = 6, f(x - i) = 52, f(x - 1) = 57 x = 116385658, i = 6, f(x - i) = 53, f(x - 1) = 58 x = 117448688, i = 6, f(x - i) = 54, f(x - 1) = 59 x = 126483083, i = 6, f(x - i) = 54, f(x - 1) = 59 x = 152523860, i = 6, f(x - i) = 55, f(x - 1) = 60 x = 189724562, i = 6, f(x - i) = 55, f(x - 1) = 60 x = 212400458, i = 6, f(x - i) = 56, f(x - 1) = 61 x = 229762259, i = 6, f(x - i) = 56, f(x - 1) = 61 x = 318689258, i = 6, f(x - i) = 57, f(x - 1) = 62 x = 348330652, i = 6, f(x - i) = 57, f(x - 1) = 62 x = 353942783, i = 6, f(x - i) = 58, f(x - 1) = 63 x = 366873514, i = 6, f(x - i) = 57, f(x - 1) = 62 x = 373603732, i = 6, f(x - i) = 57, f(x - 1) = 62 x = 379448999, i = 6, f(x - i) = 57, f(x - 1) = 62 x = 385159320, i = 8, f(x - i) = 58, f(x - 1) = 64 x = 404764540, i = 6, f(x - i) = 58, f(x - 1) = 63 x = 409108300, i = 6, f(x - i) = 58, f(x - 1) = 63 x = 460759642, i = 6, f(x - i) = 57, f(x - 1) = 62 x = 465722100, i = 8, f(x - i) = 58, f(x - 1) = 64 x = 477258719, i = 6, f(x - i) = 59, f(x - 1) = 64 x = 498197068, i = 6, f(x - i) = 58, f(x - 1) = 63 x = 511069678, i = 6, f(x - i) = 58, f(x - 1) = 63 x = 516743639, i = 6, f(x - i) = 58, f(x - 1) = 63 x = 519835084, i = 6, f(x - i) = 58, f(x - 1) = 63 x = 538858312, i = 6, f(x - i) = 59, f(x - 1) = 64 x = 545438698, i = 6, f(x - i) = 58, f(x - 1) = 63 x = 545790940, i = 6, f(x - i) = 58, f(x - 1) = 63 x = 546853138, i = 6, f(x - i) = 58, f(x - 1) = 63 x = 574842670, i = 6, f(x - i) = 58, f(x - 1) = 63 x = 575550972, i = 8, f(x - i) = 58, f(x - 1) = 64 x = 581106238, i = 6, f(x - i) = 59, f(x - 1) = 64 x = 590785918, i = 6, f(x - i) = 59, f(x - 1) = 64 x = 608504399, i = 6, f(x - i) = 60, f(x - 1) = 65 x = 612752632, i = 6, f(x - i) = 58, f(x - 1) = 63 x = 612752634, i = 8, f(x - i) = 58, f(x - 1) = 64 x = 613028608, i = 6, f(x - i) = 59, f(x - 1) = 64 x = 613175855, i = 6, f(x - i) = 59, f(x - 1) = 64 x = 614416318, i = 6, f(x - i) = 59, f(x - 1) = 64 x = 636135035, i = 6, f(x - i) = 59, f(x - 1) = 64 x = 637198964, i = 6, f(x - i) = 59, f(x - 1) = 64 x = 669796594, i = 6, f(x - i) = 59, f(x - 1) = 64 x = 673335934, i = 6, f(x - i) = 59, f(x - 1) = 64 x = 690342298, i = 6, f(x - i) = 58, f(x - 1) = 63 x = 690342300, i = 8, f(x - i) = 58, f(x - 1) = 64 x = 691406048, i = 6, f(x - i) = 59, f(x - 1) = 64 x = 692981240, i = 6, f(x - i) = 60, f(x - 1) = 65 x = 698494572, i = 8, f(x - i) = 59, f(x - 1) = 65 x = 817595279, i = 6, f(x - i) = 60, f(x - 1) = 65 x = 822093928, i = 6, f(x - i) = 60, f(x - 1) = 65 x = 833714854, i = 6, f(x - i) = 60, f(x - 1) = 65 x = 860101032, i = 6, f(x - i) = 60, f(x - 1) = 65 x = 861764920, i = 6, f(x - i) = 60, f(x - 1) = 65 x = 865717578, i = 8, f(x - i) = 59, f(x - 1) = 65 x = 919924954, i = 6, f(x - i) = 59, f(x - 1) = 64 x = 938584150, i = 6, f(x - i) = 60, f(x - 1) = 65 x = 956064164, i = 6, f(x - i) = 60, f(x - 1) = 65 x = 957480622, i = 6, f(x - i) = 60, f(x - 1) = 65 x = 969724960, i = 6, f(x - i) = 60, f(x - 1) = 65 x = 979188208, i = 6, f(x - i) = 61, f(x - 1) = 66 x = 989818648, i = 6, f(x - i) = 61, f(x - 1) = 66 x = 1010983642, i = 6, f(x - i) = 61, f(x - 1) = 66 x = 1011883067, i = 6, f(x - i) = 61, f(x - 1) = 66 x = 1033304290, i = 6, f(x - i) = 59, f(x - 1) = 64 x = 1033304292, i = 8, f(x - i) = 59, f(x - 1) = 65 x = 1034194895, i = 6, f(x - i) = 61, f(x - 1) = 66 x = 1034348380, i = 6, f(x - i) = 60, f(x - 1) = 65 x = 1034716284, i = 8, f(x - i) = 59, f(x - 1) = 65 x = 1038069034, i = 6, f(x - i) = 60, f(x - 1) = 65 x = 1039681620, i = 8, f(x - i) = 60, f(x - 1) = 66 x = 1040032000, i = 6, f(x - i) = 60, f(x - 1) = 65 x = 1042779834, i = 8, f(x - i) = 60, f(x - 1) = 66 x = 1047470290, i = 6, f(x - i) = 59, f(x - 1) = 64 x = 1058101028, i = 6, f(x - i) = 61, f(x - 1) = 66 x = 1071801000, i = 8, f(x - i) = 60, f(x - 1) = 66 x = 1088924664, i = 6, f(x - i) = 60, f(x - 1) = 65 x = 1090700242, i = 6, f(x - i) = 60, f(x - 1) = 65 x = 1091050432, i = 6, f(x - i) = 60, f(x - 1) = 65 x = 1138346747, i = 6, f(x - i) = 60, f(x - 1) = 65 x = 1140697184, i = 6, f(x - i) = 61, f(x - 1) = 66 x = 1156949240, i = 6, f(x - i) = 61, f(x - 1) = 66 x = 1163385647, i = 6, f(x - i) = 61, f(x - 1) = 66 x = 1228515840, i = 8, f(x - i) = 61, f(x - 1) = 67 x = 1247536079, i = 6, f(x - i) = 62, f(x - 1) = 67 x = 1263168935, i = 6, f(x - i) = 61, f(x - 1) = 66 x = 1272454090, i = 6, f(x - i) = 61, f(x - 1) = 66 x = 1291759578, i = 8, f(x - i) = 60, f(x - 1) = 66 x = 1308232078, i = 6, f(x - i) = 61, f(x - 1) = 66 x = 1328071184, i = 6, f(x - i) = 61, f(x - 1) = 66 x = 1378029112, i = 6, f(x - i) = 60, f(x - 1) = 65 x = 1379604848, i = 6, f(x - i) = 62, f(x - 1) = 67 x = 1380695848, i = 6, f(x - i) = 61, f(x - 1) = 66 x = 1382278338, i = 8, f(x - i) = 60, f(x - 1) = 66 x = 1383381160, i = 6, f(x - i) = 61, f(x - 1) = 66 x = 1384057332, i = 8, f(x - i) = 61, f(x - 1) = 67 x = 1397318848, i = 6, f(x - i) = 61, f(x - 1) = 66 x = 1435422222, i = 8, f(x - i) = 61, f(x - 1) = 67 x = 1436699484, i = 8, f(x - i) = 62, f(x - 1) = 68 x = 1455145810, i = 6, f(x - i) = 61, f(x - 1) = 66 x = 1457388808, i = 6, f(x - i) = 61, f(x - 1) = 66 x = 1470851984, i = 6, f(x - i) = 62, f(x - 1) = 67 x = 1472625788, i = 6, f(x - i) = 61, f(x - 1) = 66 All x, such that f(x) < min {f(x - 1) + 1} U {f(y) + f(z) | y * z = x} x = 353942783, f(x) = 63, min = 64 x = 516743639, f(x) = 63, min = 64 x = 1163385647, f(x) = 66, min = 67