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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
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, 35, 36, 37, 38, 44, 45, 47, 49, 51, 53, 55, 56, 57, 59, 60, 62, 63, 64, 65, 66, 68, 70, 71, 72, 73, 76, 78, 81, 83, 86, 89, 91, 92, 94, 98, 100, 102, 106, 108, 109 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..3000

Andrica, D., Vacaretu, D., Representation theorems and almost unimodal sequences, Studia Univ. Babes-Bolyai, Mathematica, Vol. LI, 4 (2006), 23-33.

EXAMPLE

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

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

MAPLE

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

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

         t:= b(abs(n-i^2), i-1);

         if t>1 then return 2 fi;

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

      fi

    end:

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

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

        for k while b(m, k)=0 do od;

        if b(m, k)=1 then return m fi

      od

    end:

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

CROSSREFS

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

Sequence in context: A000433 A031492 A035060 * A143719 A078779 A047593

Adjacent sequences:  A231269 A231270 A231271 * A231273 A231274 A231275

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 06 2013

STATUS

approved

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Last modified May 18 17:23 EDT 2021. Contains 343995 sequences. (Running on oeis4.)