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
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 1..261
Programs
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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