A134742 Numbers whose square is a permutational number A134640.

0, 1, 15, 50, 85, 195, 327, 561, 789, 867, 1323, 1764, 2450, 2751, 2858, 2878, 3213, 3418, 3538, 4834, 4846, 5062, 5342, 5770, 6286, 7814, 8574, 8634, 9722, 10254, 10610, 10614, 11522, 11702, 11826, 12363, 12543, 13490, 14246, 14502, 14538, 14676, 14818, 14902, 15186, 15434, 15681, 15874, 15963

Offset: 1

Author

Artur Jasinski, Nov 07 2007

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..261

Crossrefs

Cf. A134640, A134641, A134642, A134643, A134644, A023811, A134741.

Programs

Maple

N:= 10^5: # for terms <= N
extend:= proc(x,N,S,b,k)
  local i,R;
  R:= NULL;
  for i in S while x + i*b^k <= N^2 do
    if k = 0 then
       if issqr(x+i*b^k) then R:= R, sqrt(x+i*b^k) fi
    else
       R:= R, procname(x+i*b^k,N,subs(i=NULL,S),b,k-1)
    fi
  od;
  R
end proc:
f:= (b,N) -> extend(0,N,[$0..(b-1)],b,b-1):
R:= 0:
for b from 2 while b^(b-2) < N^2 do
  R:= R, f(b,N);
od:
sort([R]); # Robert Israel, Sep 04 2020

Mathematica

a = {}; b = {}; Do[AppendTo[b, n]; w =Permutations[b]; Do[j = FromDigits[w[[m]], n + 1]; If[IntegerQ[j^(1/2)], AppendTo[a, j]], {m, 1, Length[w]}], {n, 0, 7}]; Sqrt[a]

Formula

a(n) = sqrt(A134741(n)).

Extensions

Corrected and more terms from Robert Israel, Sep 04 2020