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.
1, 11, 111, 1111, 11111, 111111, 1111111, 3648169, 3649816, 3681649, 3698164, 8163649, 8164369, 8164936, 8169364, 9364816, 9368164, 9816364, 9816436, 11111111, 13648169, 13649816, 13681649, 13698164, 16364819, 16364981
Offset: 1
Examples
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.
Links
- Robert G. Wilson v, Table of n, a(n) for n = 1..11523 (first 300 terms from David Applegate)
Programs
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Mathematica
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 *) -
Python
sq = {d:str(int(d)**2) for d in "123456789"} def ok(n): return "0" not in (s:=str(n)) and all(sq[d] in s for d in set(s)) print([k for k in range(10**7) if ok(k)]) # Michael S. Branicky, May 05 2023
Extensions
a(9) onwards computed by David Applegate, Feb 03 2008
Comments