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A119509 Positive numbers whose square contains no digit more than once. 6

%I #40 Nov 28 2022 01:47:00

%S 1,2,3,4,5,6,7,8,9,13,14,16,17,18,19,23,24,25,27,28,29,31,32,33,36,37,

%T 42,43,44,48,49,51,52,53,54,55,57,59,61,64,66,69,71,72,73,74,78,79,82,

%U 84,86,87,89,93,95,96,98,99,113,116,117,118,124,126,128,133

%N Positive numbers whose square contains no digit more than once.

%C There are exactly 610 terms. a(610) = 99066 and 99066^2 = 9814072356. - _Rick L. Shepherd_, Jul 27 2006

%C If we count 0, there is one more term, for a total of 611. - _T. D. Noe_, Jun 21 2013

%H Rick L. Shepherd, <a href="/A119509/b119509.txt">Table of n, a(n) for n = 1..610</a> (full sequence)

%p lim:=floor(sqrt(9876543210)): A119509:={}: for n from 1 to lim do pandig:=true: d:=convert(n^2,base,10): for k from 0 to 9 do if(numboccur(k, d)>1)then pandig:=false: break: fi: od: if(pandig)then A119509 := A119509 union {n}: fi: od: op(sort(convert(A119509,list))); # _Nathaniel Johnston_, Jun 23 2011

%t Select[Range[1000000], Length[IntegerDigits[ # ^2]] == Length[Union[IntegerDigits[ # ^2]]] &] (* _Tanya Khovanova_, May 29 2007 *)

%t Select[Range[10^5], Max[DigitCount[#^2]] <= 1 &] (* _T. D. Noe_, Aug 02 2011 *)

%o (Magma) [n: n in [1..10^5] | #Set(d) eq #d where d is Intseq(n^2)]; // _Bruno Berselli_, Aug 02 2011

%o (PARI) is_A119509(n)=#(n=digits(n^2))==#Set(n) \\ _M. F. Hasler_, Sep 08 2017

%o (Python)

%o def ok(n): s = str(n**2); return n > 0 and len(set(s)) == len(s)

%o afull = [k for k in range(10**5) if ok(k)] # _Michael S. Branicky_, Nov 27 2022

%Y Subsequence of A045540 = numbers whose squares contain an equal number of each digit that they contain. The first number that belongs to A045540 and doesn't belong to this sequence is number 88.

%Y Cf. A078255, A036745, A075309, A162950.

%K base,fini,full,nonn

%O 1,2

%A _Tanya Khovanova_, Jul 26 2006

%E More terms from _Rick L. Shepherd_, Jul 27 2006

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)