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

1,3

Links

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

Formula

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

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]

Crossrefs

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

Sequence in context: A298511 A349855 A103777 * A318084 A191746 A029941

Adjacent sequences: A134739 A134740 A134741 * A134743 A134744 A134745

Keyword

nonn

Author

Artur Jasinski, Nov 07 2007

Extensions

Corrected and more terms from Robert Israel, Sep 04 2020

Status

approved