1,4

Positions of first 20 numbers in the sequence: {1:{1, 2, 3, 5, 11, 42, 57, 141, 709, 1119, 1223, 1333}}, {2:{4, 6, 12, 43, 58, 142, 710, 1120, 1224, 1334}}, {3:{8, 24, 49, 53, 683, 1550}}, {4:{7, 13, 44, 59, 143, 711, 1121, 1225, 1335}}, {5:{10, 15, 32, 39, 220, 361, 402, 562, 672}}, {6:{9, 25, 50, 54, 684, 1551}}, {7:{17, 35, 99, 188, 353, 1156, 1630}}, {8:{14, 45, 60, 144, 712, 1122, 1226, 1336}}, {9:{20, 30, 65, 164, 236, 723}}, {10:{16, 33, 40, 221, 362, 403, 563, 673}}, {11:{76, 277, 333}}, {12:{26, 51, 55, 685, 1552}}, {13:{19, 23, 318, 338}}, {14:{18, 36, 100, 189, 354, 1157, 1631}}, {15:{63, 430, 613, 1541, 1754}}, {16:{46, 61, 145, 713, 1123, 1227, 1337}}, {17:{22, 107, 158, 325, 1914}}, {18:{21, 31, 66, 165, 237, 724}}, {19:{29, 68, 103}}, {20:{34, 41, 222, 363, 404, 564, 674}}. From the first 2000 terms, the first absent numbers are: 67,105,109,134,148,152,168,183,187,193,199. Do all numbers, except zero, appear eventually in the sequence? Do ones appear infinitely many times?

Zak Seidov, Table of n, a(n) for n = 1..2000

a(1)=a(2)=1; for n>2: a(n)=s-(floor(sqrt(s)))^2, where s=sum (a(i), i=1..n-1).

a={1, 1}; s=2; Do[b=s-(Floor[Sqrt[s]])^2; AppendTo[a, b]; s=s+b, {2000}]; a

Sequence in context: A131380 A100461 A124904 this_sequence A105022 A105970 A133950

Adjacent sequences: A129141 A129142 A129143 this_sequence A129145 A129146 A129147

nonn

Zak Seidov (zakseidov(AT)gmail.com), Mar 31 2007