

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. BabesBolyai, Mathematica, Vol. LI, 4 (2006), 2333.


EXAMPLE

10 is member of the sequence with unique minimal solution 10 = 1+49+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(ni^2), i1);
if t>1 then return 2 fi;
t:= t+b(n+i^2, i1); `if`(t>1, 2, t)
fi
end:
a:= proc(n) option remember; local m, k;
for m from 1+ `if`(n=1, 1, a(n1)) 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



