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A053057
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Squares whose digit sum is also a square.
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13
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0, 1, 4, 9, 36, 81, 100, 121, 144, 169, 196, 225, 324, 400, 441, 484, 529, 900, 961, 1521, 1681, 2025, 2304, 2601, 3364, 3481, 3600, 4489, 4624, 5776, 5929, 7225, 7396, 8100, 8836, 9025, 10000, 10201, 10404, 10609, 10816, 11025, 12100, 12321, 12544, 12769
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OFFSET
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1,3
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COMMENTS
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The numbers 81, 100, 121, 144, 169, 196, 225 are seven consecutive squares belonging to this sequence. The next set of seven consecutive squares whose digit sum is also a square is {9999^2, 10000^2, 10001^2, 10002^2, 10003^2, 10004^2, 10005^2}. (See Crux Mathematicorum link.) - Bernard Schott, May 24 2017
The first set of 8 consecutive squares begin at 46045846^2. This was already known in 2016, see MathStackExchange link. - Michel Marcus, May 25 2017
The first run of 9 consecutive squares starts at 302260461719025^2. - Giovanni Resta, Jun 08 2017
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REFERENCES
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Felice Russo, A set of new Smarandache functions, sequences and conjectures in number theory, American Research Press, 2000.
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LINKS
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Allan Wm. Johnson Jr., Problem 443, Crux Mathematicorum, Vol. 6, No. 3 (Mar. 1980), page 88.
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EXAMPLE
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144 is a term: 144 = 12^2 and 1 + 4 + 4 = 9 = 3^2. - Bernard Schott, May 24 2017
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MATHEMATICA
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Select[Range[0, 115]^2, IntegerQ[Sqrt[DigitSum[#]]]&] (* Stefano Spezia, Mar 07 2024 *)
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PROG
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(Magma) [n^2: n in [0..120] | IsSquare(&+Intseq(n^2))]; // Bruno Berselli, May 26 2011
(PARI) lista(nn) = for (n=1, nn, if (issquare(sumdigits(n^2)), print1(n^2, ", ")); ); \\ Michel Marcus, May 25 2017
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CROSSREFS
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KEYWORD
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nonn,easy,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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