A129144 a(1)=a(2)=1; for n>2: a(n) = (s = sum of all previous terms) minus (maximal square less than s).

1, 1, 1, 2, 1, 2, 4, 3, 6, 5, 1, 2, 4, 8, 5, 10, 7, 14, 13, 9, 18, 17, 13, 3, 6, 12, 24, 23, 19, 9, 18, 5, 10, 20, 7, 14, 28, 21, 5, 10, 20, 1, 2, 4, 8, 16, 32, 23, 3, 6, 12, 24, 3, 6, 12, 24, 1, 2, 4, 8, 16, 32, 15, 30, 9, 18, 36, 19, 38, 21, 42, 27, 54, 49, 37, 11, 22, 44, 23, 46, 25, 50

Offset

1,4

Comments

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?

Links

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

Formula

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

Mathematica

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

Crossrefs

Sequence in context: A124904 A187500 A323460 * A360594 A295313 A105022

Adjacent sequences: A129141 A129142 A129143 * A129145 A129146 A129147

Keyword

nonn

Author

Zak Seidov, Mar 31 2007

Status

approved