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A231272 Numbers n with unique solution to n = +-1^2+-2^2+-3^2+-4^2+-...+-k^2 with minimal k giving at least one solution. 4


%S 1,2,3,4,5,6,7,10,11,12,13,14,15,17,19,20,21,22,23,24,26,27,28,29,30,

%T 35,36,37,38,44,45,47,49,51,53,55,56,57,59,60,62,63,64,65,66,68,70,71,

%U 72,73,76,78,81,83,86,89,91,92,94,98,100,102,106,108,109

%N Numbers n with unique solution to n = +-1^2+-2^2+-3^2+-4^2+-...+-k^2 with minimal k giving at least one solution.

%C Numbers n such that A231071(n) = 1. The value of k is given by A231015(n).

%H Alois P. Heinz, <a href="/A231272/b231272.txt">Table of n, a(n) for n = 1..3000</a>

%H Andrica, D., Vacaretu, D., <a href="http://www.cs.ubbcluj.ro/~studia-m/2006-4/andrica.pdf">Representation theorems and almost unimodal sequences</a>, Studia Univ. Babes-Bolyai, Mathematica, Vol. LI, 4 (2006), 23-33.

%e 10 is member of the sequence with unique minimal solution 10 = -1+4-9+16.

%e A000330(k) = k(k+1)(2k+1)/6 = 1^2 + 2^2 + ... + k^2 is a member for k > 0. - _Jonathan Sondow_, Nov 06 2013

%p b:= proc(n, i) option remember; local m, t; m:= (1+(3+2*i)*i)*i/6;

%p if n>m then 0 elif n=m then 1 else

%p t:= b(abs(n-i^2), i-1);

%p if t>1 then return 2 fi;

%p t:= t+b(n+i^2, i-1); `if`(t>1, 2, t)

%p fi

%p end:

%p a:= proc(n) option remember; local m, k;

%p for m from 1+ `if`(n=1, -1, a(n-1)) do

%p for k while b(m, k)=0 do od;

%p if b(m, k)=1 then return m fi

%p od

%p end:

%p seq(a(n), n=1..80);

%Y Cf. A000330, A231015, A231071, A231016 (complement).

%K nonn

%O 1,2

%A _Alois P. Heinz_, Nov 06 2013

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Last modified January 19 00:40 EST 2020. Contains 331030 sequences. (Running on oeis4.)