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%I #10 Sep 04 2020 21:23:04
%S 0,1,225,2500,7225,38025,106929,314721,622521,751689,1750329,3111696,
%T 6002500,7568001,8168164,8282884,10323369,11682724,12517444,23367556,
%U 23483716,25623844,28536964,33292900,39513796,61058596,73513476,74545956,94517284,105144516,112572100,112656996,132756484
%N Permutational numbers A134640 which are squares.
%H Robert Israel, <a href="/A134741/b134741.txt">Table of n, a(n) for n = 1..261</a>
%F a(n) = A134742(n)^2.
%p N:= 10^10: # for terms <= N
%p extend:= proc(x, N, S, b, k)
%p local i, R;
%p R:= NULL;
%p for i in S while x + i*b^k <= N do
%p if k = 0 then
%p if issqr(x+i*b^k) then R:= R, x+i*b^k fi
%p else
%p R:= R, procname(x+i*b^k, N, subs(i=NULL, S), b, k-1)
%p fi
%p od;
%p R
%p end proc:
%p f:= (b, N) -> extend(0, N, [$0..(b-1)], b, b-1):
%p R:= 0:
%p for b from 2 while b^(b-2) < N do
%p R:= R, f(b, N);
%p od:
%p sort([R]); # Robert Israel, Sep 04 2020
%t 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
%Y Cf. A134640, A134641, A134642, A134643, A134644, A023811, A134742.
%K nonn
%O 1,3
%A _Artur Jasinski_, Nov 07 2007
%E Corrected and more terms from _Robert Israel_, Sep 04 2020
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