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A119509
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Numbers whose square contains no repeated digit.
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3
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| There are exactly 610 terms. a(610) = 99066 and 99066^2 = 9814072356. - Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jul 27 2006
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LINKS
| Rick L. Shepherd, Table of n, a(n) for n = 1..610
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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
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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 *)
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PROG
| (MAGMA) [n: n in [1..10^5] | #Set(d) eq #d where d is Intseq(n^2)]; // Bruno Berselli, Aug 02 2011
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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 * A055568 A165165 A075776
Adjacent sequences: A119506 A119507 A119508 * A119510 A119511 A119512
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KEYWORD
| base,fini,nonn
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AUTHOR
| Tanya Khovanova (tanyakh(AT)yahoo.com), Jul 26 2006
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EXTENSIONS
| More terms from Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jul 27 2006
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