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Search: id:A077439
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| A077439 |
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Numbers n such that n and n^2 have square decimal digits. |
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+0
2
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| 0, 1, 10, 100, 1000, 1049, 10000, 10490, 100000, 100499, 104900, 1000000, 1004990, 1049000, 10000000, 10004999, 10049900, 10490000, 100000000, 100049990, 100499000, 104900000, 1000000000, 1000049999, 1000499900, 1004990000, 1044049999, 1049000000, 10000000000, 10000499990, 10004999000, 10049900000, 10440499990
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Numbers n such that n and the square of n use only the digits 0, 1, 4 and 9.
Notice the trick used in the Mathematica program to convert decimal numbers to base 4 numbers and then map threes into nines and then twos into fours. This saves a lot of computing. - Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 08 2002
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LINKS
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Jonathan Wellons, Table of n, a(n) for n=1..68
J. Wellons, Tables of Shared Digits
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EXAMPLE
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1049^2 = 1100401, therefore 1049 is a term; whereas A046030(6)=14 is not a term, as 14^2=196 and 6 is not a square digit.
104900499999000^2 = 11004114900040199000001000000
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MATHEMATICA
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a = {}; Do[d = FromDigits[ ReplaceAll[ IntegerDigits[n, 4], {3 -> 9, 2 -> 4}]]; If[ Union[ Join[ IntegerDigits[d^2], {0, 1, 4, 9}]] == {0, 1, 4, 9}, a = Append[a, d]], {n, 0, 3*10^5}]; a
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CROSSREFS
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A077440(n) = a(n)^2.
Cf. A046030, A019544, A000290.
Sequence in context: A055992 A115814 A115798 this_sequence A136839 A136863 A031201
Adjacent sequences: A077436 A077437 A077438 this_sequence A077440 A077441 A077442
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KEYWORD
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base,nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 06 2002
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EXTENSIONS
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Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 08 2002
More terms from Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008
Edited by N. J. A. Sloane (njas(AT)research.att.com), May 15 2008 at the suggestion of R. J. Mathar.
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