

A119509


Positive numbers whose square contains no digit more than once.


6



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, 42, 43, 44, 48, 49, 51, 52, 53, 54, 55, 57, 59, 61, 64, 66, 69, 71, 72, 73, 74, 78, 79, 82, 84, 86, 87, 89, 93, 95, 96, 98, 99, 113, 116, 117, 118, 124, 126, 128, 133
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OFFSET

1,2


COMMENTS

There are exactly 610 terms. a(610) = 99066 and 99066^2 = 9814072356.  Rick L. Shepherd, Jul 27 2006
If we count 0, there is one more term, for a total of 611.  T. D. Noe, Jun 21 2013


LINKS

Rick L. Shepherd, Table of n, a(n) for n = 1..610 (full sequence)


MAPLE

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


MATHEMATICA

Select[Range[1000000], Length[IntegerDigits[ # ^2]] == Length[Union[IntegerDigits[ # ^2]]] &] (* Tanya Khovanova, May 29 2007 *)
Select[Range[10^5], Max[DigitCount[#^2]] <= 1 &] (* T. D. Noe, Aug 02 2011 *)


PROG

(MAGMA) [n: n in [1..10^5]  #Set(d) eq #d where d is Intseq(n^2)]; // Bruno Berselli, Aug 02 2011
(PARI) is_A119509(n)=#(n=digits(n^2))==#Set(n) \\ M. F. Hasler, Sep 08 2017


CROSSREFS

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.
Cf. A078255, A036745, A075309, A162950.
Sequence in context: A135140 A052061 A045540 * A219248 A055568 A283161
Adjacent sequences: A119506 A119507 A119508 * A119510 A119511 A119512


KEYWORD

base,fini,full,nonn


AUTHOR

Tanya Khovanova, Jul 26 2006


EXTENSIONS

More terms from Rick L. Shepherd, Jul 27 2006


STATUS

approved



