cp's OEIS Frontend

A294661 Numbers whose square contains all of the digits 1 through 9.

%I A294661 #12 Mar 26 2021 08:38:57
%S A294661 11826,12363,12543,14676,15681,15963,18072,19023,19377,19569,19629,
%T A294661 20316,22887,23019,23178,23439,24237,24276,24441,24807,25059,25572,
%U A294661 25941,26409,26733,27129,27273,29034,29106,30384,32043,32286,33144,34273,35172,35337,35713,35756,35757,35772,35846,35853
%N A294661 Numbers whose square contains all of the digits 1 through 9.
%C A294661 The sequence has asymptotic density 1: it contains "almost all" numbers.
%H A294661 Amiram Eldar, <a href="/A294661/b294661.txt">Table of n, a(n) for n = 1..10000</a>
%e A294661 11826^2 = 139854276 contains all digits from 1 to 9 exactly once.
%e A294661 The same is true for all terms up to 30384 whose square is 923187456. These terms are also listed in A071519, they form a subsequence of A054037.
%e A294661 The next 3 terms, 32043 (32043^2 = 1026753849), 32286 (32286^2 = 1042385796) and 33144 (33144^2 = 1098524736) contain all of the digits '0' through '9' exactly once: They are the first terms of A054038.
%e A294661 The next term, 34273 with 34273^2 = 1174638529, does not have this property, but the next two are again of that type (35172^2 = 1237069584 and 35337^2 = 1248703569).
%t A294661 Select[Range[#, # + 3*10^4] &@ 11111, AllTrue[Most@ DigitCount[#^2], # > 0 &] &] (* _Michael De Vlieger_, Nov 08 2017 *)
%o A294661 (PARI) is_A294661(n)=#select(t->t,Set(digits(n^2)))>8
%o A294661 N=100;for(k=10^4,oo,is_A294661(k)||next;print1(k",");N--||break)
%Y A294661 Cf. A054037, A071519 (finite subsequence of the first 30 terms), A054038.
%K A294661 nonn,base
%O A294661 1,1
%A A294661 _M. F. Hasler_, Nov 08 2017