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

1,3

Links

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

Formula

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

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

Crossrefs

Cf. A134640, A134641, A134642, A134643, A134644, A023811, A134742.

Sequence in context: A105925 A014771 A184878 * A110204 A180697 A230065

Adjacent sequences: A134738 A134739 A134740 * A134742 A134743 A134744

Keyword

nonn

Author

Artur Jasinski, Nov 07 2007

Extensions

Corrected and more terms from Robert Israel, Sep 04 2020

Status

approved