

A259018


Lexicographically first permutation of the nonnegative integers such that Sum_{k=n..2n} a(k) is a square, starting with a(1)=0.


1



0, 1, 2, 6, 3, 5, 4, 7, 8, 9, 10, 21, 11, 30, 12, 13, 14, 16, 15, 18, 17, 19, 20, 50, 22, 32, 23, 60, 24, 45, 25, 28, 26, 75, 27, 34, 29, 36, 31, 35, 33, 38, 37, 92, 39, 100, 40, 43, 41, 74, 42, 47, 44, 57, 46, 48, 49, 84, 51, 52, 53, 90, 54, 55, 56, 58, 93, 59
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OFFSET

1,3


COMMENTS

The corresponding squares are 1, 9, 16, 25, 36, 64, 100, 121, 144, 169, 196, 256, 289, 361, 400, 441, 529, 576, 625, 676, 729, 841, 961, 1024, 1089, 1156, 1225, 1296, 1369, ...
This is a permutation of the integers.


LINKS



EXAMPLE

a(1) = 0 plus the next single term 1 is 1 = 1^2;
a(2) = 1 plus the next two terms (2,6) is 9 = 3^2;
a(3) = 2 plus the next three terms (6,3,5) is 16 = 4^2;
a(4) = 6 plus the next four terms (3,5,4,7) is 25 = 5^2.


MAPLE

nn:=100:T:=array(1..nn):T[1]:=0:T[2]:=1:kk:=2:lst:={0, 1}:
for n from 2 to nn do:
ii:=0:
for k from 2 to 1000 while(ii=0)do:
if {k} intersect lst = {}
then
ii:=1:lst:=lst union {k}:kk:=kk+1:T[kk]:=k:
else
fi:
od:
jj:=0:n0:=nops(lst):s:=sum('T[i]', 'i'=n..n0):
for p from 1 to 100 while(jj=0) do:
z:=sqrt(s+p):
if z = floor(z) and {p} intersect lst={}
then
jj:=1:lst:=lst union {p}:kk:=kk+1:T[kk]:=p:
else
fi:
od:
od:
print(T):


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



