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Search: id:A036744
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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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1
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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; listen)
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OFFSET
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1,1
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COMMENT
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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
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MATHEMATICA
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Select[Range[11112, 31427]^2, Union[Drop[DigitCount[ # ], -1]] == {1} &]
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CROSSREFS
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Adjacent sequences: A036741 A036742 A036743 this_sequence A036745 A036746 A036747
Sequence in context: A105297 A034642 A109093 this_sequence A075130 A034611 A160688
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KEYWORD
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fini,nonn,full
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
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More terms from Harvey P. Dale (hpd1(AT)nyu.edu), Sep 26 2001
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