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

Author

Michel Lagneau, Jun 16 2015

Keywords

• nonn

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.

Examples

			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.
		

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000290, A247665.

Programs

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):