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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 (list; graph; refs; listen; history; text; internal format)
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
Subsequence of A000290.
Sequence in context: A267430 A117756 A326182 * A118547 A363408 A115700
KEYWORD
nonn,easy,base
AUTHOR
Felice Russo, Feb 25 2000
EXTENSIONS
More terms from James A. Sellers, Feb 28 2000
STATUS
approved

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Last modified April 20 21:11 EDT 2024. Contains 371845 sequences. (Running on oeis4.)