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A008319
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Smallest number that is sum of squares of distinct earlier terms.
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0
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1, 1, 2, 4, 5, 6, 16, 17, 18, 20, 21, 22, 25, 26, 27, 29, 30, 31, 36, 37, 38, 40, 41, 42, 43, 45, 46, 47, 52, 53, 54, 56, 57, 58, 61, 62, 63, 65, 66, 67, 77, 78, 79, 81, 82, 83, 256, 257, 258, 260, 261, 262, 272, 273, 274, 276, 277, 278, 281, 282, 283, 285, 286, 287, 289, 290, 291
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Up to a(99999680)=10^8, the largest number not in the sequence is 892. I also computed, up to a(99934078)=10^8, the similar sequence which starts with 1,2 instead of 1,1. The largest number not in that sequence seems to be 134179 - Giovanni Resta (g.resta(AT)iit.cnr.it), Oct 06 2011
Resta's conjecture is correct. Let x = floor(sqrt(n) - 12). For n > 1935, x^2 > n/2. For n > 1853, n - x^2 > 892. So n > 1935 can be decomposed into x^2 plus a number greater than 892. Since the other number is smaller than x^2, any decomposition into squares will use only numbers smaller than x. By induction, all numbers greater than 1935 (and hence greater than 892) are in this sequence. [Charles R Greathouse IV, Oct 06 2011]
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REFERENCES
| F. Smarandache, Definitions solved and unsolved problems, conjectures and theorems in number theory and geometry, edited by M. Perez, Xiquan Publishing House 2000
M. Bencze, Smarandache Recurrence Type Sequences, Bull. Pure Appl. Sciences, Vol. 16E, No. 2 (1997), pp. 231-236.
F. Smarandache, Sequences of Numbers Involved in Unsolved Problems, Hexis, Phoenix, 2006.
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LINKS
| F. Smarandache, Definitions, Solved and Unsolved Problems, Conjectures, ...
Eric Weisstein's World of Mathematics, Smarandache Sequences
More information
F. Smarandache, Sequences of Numbers Involved in Unsolved Problems.
Index to sequences with linear recurrences with constant coefficients, signature (2,-1).
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FORMULA
| For n > 572, a(n) = n + 320. [Charles R Greathouse IV, Oct 06 2011]
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CROSSREFS
| Sequence in context: A191165 A058637 A026473 * A033311 A098504 A137653
Adjacent sequences: A008316 A008317 A008318 * A008320 A008321 A008322
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KEYWORD
| nonn,easy,nice
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AUTHOR
| R. Muller
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EXTENSIONS
| More terms from David W. Wilson (davidwwilson(AT)comcast.net)
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