

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
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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. 231236.


LINKS

Table of n, a(n) for n=1..67.
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



