

A053057


Squares whose digit sum is also a square.


13



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

1,3


COMMENTS

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


REFERENCES

Felice Russo, A set of new Smarandache functions, sequences and conjectures in number theory, American Research Press, 2000.


LINKS

Allan Wm. Johnson Jr., Problem 443, Crux Mathematicorum, Vol. 6, No. 3 (Mar. 1980), page 88.


EXAMPLE

144 is a term: 144 = 12^2 and 1 + 4 + 4 = 9 = 3^2.  Bernard Schott, May 24 2017


MATHEMATICA

Select[Range[0, 115]^2, IntegerQ[Sqrt[DigitSum[#]]]&] (* Stefano Spezia, Mar 07 2024 *)


PROG

(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


CROSSREFS



KEYWORD

nonn,easy,base


AUTHOR



EXTENSIONS



STATUS

approved



