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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, 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 (list; graph; refs; listen; history; text; internal format)
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 * A295313 A105022 A263293

Adjacent sequences:  A129141 A129142 A129143 * A129145 A129146 A129147

KEYWORD

nonn

AUTHOR

Zak Seidov, Mar 31 2007

STATUS

approved

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Last modified September 25 13:01 EDT 2020. Contains 337344 sequences. (Running on oeis4.)