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A036744
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Penholodigital squares: squares containing each of the digits 1..9 exactly once.
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2
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139854276, 152843769, 157326849, 215384976, 245893761, 254817369, 326597184, 361874529, 375468129, 382945761, 385297641, 412739856, 523814769, 529874361, 537219684, 549386721, 587432169, 589324176, 597362481, 615387249, 627953481, 653927184, 672935481, 697435281, 714653289, 735982641, 743816529, 842973156, 847159236, 923187456
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Improved Mathematica formula provided. Because the range involved is only from Ceiling[Sqrt[123456789]]=11112 and Floor[Sqrt[987654321]]=31427, it only requires analyzing 20,315 numbers, versus 362,880 permutations of nine digits (as in the current formula). - Harvey P. Dale (hpd1(AT)nyu.edu), Apr 17 2002
Since the sum of the digits is 45, the squares are all divisible by 3, so the given Mathematica formula could be sped up by a factor of 3, checking only multiples of 3 rather than all squares. - Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), Nov 28 2005
Eight-digit analog gives 5 squares:
13527684, 34857216, 65318724, 73256481, 81432576.
- Zak Seidov Mar 01 2011
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FORMULA
| a(n) = A071519(n)^2.
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MAPLE
| lim:=floor(sqrt(987654321)): for n from 11112 by 3 to lim do d:=[op(convert(n^2, base, 10))]: pandig:=true: for k from 1 to 9 do if(numboccur(k, d)<>1)then pandig:=false: break: fi: od: if(pandig)then printf("%d, ", n^2): fi: od: # Nathaniel Johnston, Jun 22 2011
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MATHEMATICA
| Select[Range[11112, 31427]^2, Union[Drop[DigitCount[ # ], -1]] == {1} &]
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CROSSREFS
| Cf. A036745, A071519.
Sequence in context: A203505 A034642 A109093 * A075130 A202280 A034611
Adjacent sequences: A036741 A036742 A036743 * A036745 A036746 A036747
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KEYWORD
| nonn,base,fini,full
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
| More terms from Harvey P. Dale (hpd1(AT)nyu.edu), Sep 26 2001
Keyword base added by Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 16 2010
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