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 A008319 Smallest number that is sum of squares of distinct earlier terms. 0
 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; text; internal format)
 OFFSET 1,3 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, 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 REFERENCES Mihaly Bencze [Beneze], Smarandache Recurrence Type Sequences, Bull. Pure Appl. Sciences, Vol. 16E, No. 2 (1997), pp. 231-236. LINKS F. Smarandache, Definitions, Solved and Unsolved Problems, Conjectures, ... F. Smarandache, Sequences of Numbers Involved in Unsolved Problems. Eric Weisstein's World of Mathematics, Smarandache Sequences Index entries for linear recurrences with constant coefficients, signature (2,-1). FORMULA For n > 572, a(n) = n + 320. - Charles R Greathouse IV, Oct 06 2011 CROSSREFS Sequence in context: A058637 A026473 A272929 * A033311 A098504 A137653 Adjacent sequences:  A008316 A008317 A008318 * A008320 A008321 A008322 KEYWORD nonn,easy,nice AUTHOR R. Muller EXTENSIONS More terms from David W. Wilson STATUS approved

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Last modified December 16 06:18 EST 2019. Contains 330016 sequences. (Running on oeis4.)