A134741 Permutational numbers A134640 which are squares.

0, 1, 225, 2500, 7225, 38025, 106929, 314721, 622521, 751689, 1750329, 3111696, 6002500, 7568001, 8168164, 8282884, 10323369, 11682724, 12517444, 23367556, 23483716, 25623844, 28536964, 33292900, 39513796, 61058596, 73513476, 74545956, 94517284, 105144516, 112572100, 112656996, 132756484

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, A134742.

Programs

Maple

N:= 10^10: # 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 do
    if k = 0 then
       if issqr(x+i*b^k) then R:= R, 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 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}]; a

Formula

a(n) = A134742(n)^2.

Extensions

Corrected and more terms from Robert Israel, Sep 04 2020