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Smallest number that is not the sum of squares of distinct earlier terms.
1

%I #22 Feb 21 2014 23:04:00

%S 1,2,3,6,7,8,11,12,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,

%T 32,33,34,35,38,39,42,43,44,47,48,51,52,55,56,57,60,61,66,67,70,71,72,

%U 75,76,79,80,81,82,83,84,87,88,91,92,93,96,97,102,103,106,107,108,111,112,115

%N Smallest number that is not the sum of squares of distinct earlier terms.

%C There is an isolated large gap between a(166) = 516 and a(167) = 6599859.

%C a(n) = n + 6600044 on the precise range 332 <= n <= 43558132219836.

%D Mihaly Bencze [Beneze], Smarandache Recurrence Type Sequences, Bull. Pure Appl. Sciences, Vol. 16E, No. 2 (1997), pp. 231-236.

%D F. Smarandache, Definitions solved and unsolved problems, conjectures and theorems in number theory and geometry, edited by M. Perez, Xiquan Publishing House, 2000.

%D F. Smarandache, Sequences of Numbers Involved in Unsolved Problems, Hexis, Phoenix, 2006.

%H David W. Wilson, <a href="/A008321/b008321.txt">Table of n, a(n) for n = 1..10000</a>

%H F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/Definitions-book.pdf">Definitions, Solved and Unsolved Problems, Conjectures, ... </a>

%H F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/Sequences-book.pdf">Sequences of Numbers Involved in Unsolved Problems</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SmarandacheSequences.html">Smarandache Sequences.</a>

%e 59 is not in the sequence because it is a sum of squares of terms smaller than 59: 1^2 + 3^2 + 7^2.

%K nonn

%O 1,2

%A R. Muller

%E More terms from _David W. Wilson_