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A134962 Numbers n with property that for each single digit d of n, we can also see the decimal expansion of d^2 as a substring of n. Also n may not contain any 0 digits.

%I A134962 #21 May 06 2023 04:21:32
%S A134962 1,11,111,1111,11111,111111,1111111,3648169,3649816,3681649,3698164,
%T A134962 8163649,8164369,8164936,8169364,9364816,9368164,9816364,9816436,
%U A134962 11111111,13648169,13649816,13681649,13698164,16364819,16364981
%N A134962 Numbers n with property that for each single digit d of n, we can also see the decimal expansion of d^2 as a substring of n. Also n may not contain any 0 digits.
%C A134962 The number of terms less than 10^k: 1, 2, 3, 4, 5, 6, 19, 410, 8083, ... . - _Robert G. Wilson v_, Jan 06 2012
%H A134962 Robert G. Wilson v, <a href="/A134962/b134962.txt">Table of n, a(n) for n = 1..11523</a> (first 300 terms from David Applegate)
%e A134962 In 3648169, for 3 we can see 9, for 6 we can see 36, for 4 we can see 16, for 8 we can see 64, for 1 we can see 1 and for 9 we can see 81.
%t A134962 fQ[n_] := (id = IntegerDigits@ n; Union[id][[1]] != 0 && Sort[ StringPosition[ ToString[n], ToString[#]] & /@ Evaluate[ id^2]][[1]] != {}); k = 0; lst = {}; While[k < 2*10^7, If[fQ@k, AppendTo[lst, k]; Print@ k]; k++] (* _Robert G. Wilson v_, Jan 06 2012 *)
%o A134962 For C++ program, see the Applegate link in A135463.
%o A134962 (Python)
%o A134962 sq = {d:str(int(d)**2) for d in "123456789"}
%o A134962 def ok(n): return "0" not in (s:=str(n)) and all(sq[d] in s for d in set(s))
%o A134962 print([k for k in range(10**7) if ok(k)]) # _Michael S. Branicky_, May 05 2023
%Y A134962 Cf. A134439, A134692, A134698, A135463, A135464.
%K A134962 nonn,base
%O A134962 1,2
%A A134962 _Zak Seidov_ and _N. J. A. Sloane_, Feb 03 2008
%E A134962 a(9) onwards computed by _David Applegate_, Feb 03 2008