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
KEYWORD
nonn,easy,nice
AUTHOR
R. Muller
EXTENSIONS
More terms from David W. Wilson
STATUS
approved