A259018 Lexicographically first permutation of the nonnegative integers such that Sum_{k=n..2n} a(k) is a square, starting with a(1)=0.

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

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

Table of n, a(n) for n=1..68.

Index entries for sequences that are permutations of the natural numbers

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

Cf. A000290, A247665.

Sequence in context: A258252 A351496 A154048 * A353649 A084355 A093650

Adjacent sequences: A259015 A259016 A259017 * A259019 A259020 A259021

Keyword

nonn

Author

Michel Lagneau, Jun 16 2015

Status

approved