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A048653 Numbers n such that the decimal digits of n^2 can be partitioned into two or more squares. 3
7, 12, 13, 19, 21, 35, 37, 38, 41, 44, 57, 65, 70, 107, 108, 112, 119, 120, 121, 125, 129, 130, 190, 191, 204, 205, 209, 210, 212, 223, 253, 285, 305, 306, 315, 342, 343, 345, 350, 369, 370, 379, 380, 408, 410, 413, 440, 441, 475, 487, 501, 538, 570, 642, 650 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

EXAMPLE

12 is present because 12^2=144 can be partitioned into three squares 1, 4 and 4.

108^2 = 11664 = 1_16_64, 120^2 = 14400 = 1_4_400, so 108 and 120 are in the sequence.

MATHEMATICA

(* This non-optimized program is not suitable to compute a large number of terms. *) split[digits_, pos_] := Module[{pos2}, pos2 = Transpose[{Join[ {1}, Most[pos+1]], pos}]; FromDigits[Take[digits, {#[[1]], #[[2]]}]]& /@ pos2]; sel[n_] := Module[{digits, ip, ip2, accu, nn}, digits = IntegerDigits[n^2]; ip = IntegerPartitions[Length[digits]]; ip2 = Flatten[ Permutations /@ ip, 1]; accu = Accumulate /@ ip2; nn = split[ digits, #]& /@ accu; SelectFirst[nn, Length[#]>1 && Flatten[ IntegerDigits[#] ] == digits && AllTrue[#, #>0 && IntegerQ[Sqrt[#]]&]&] ]; k = 1; Reap[Do[If[(s = sel[n]) != {}, Print["a(", k++, ") = ", n, " ", n^2, " ", s]; Sow[n]], {n, 1, 10^4}]][[2, 1]] (* Jean-Fran├žois Alcover, Sep 28 2016 *)

PROG

(Haskell)

a048653 n = a048653_list !! (n-1)

a048653_list = filter (f . show . (^ 2)) [1..] where

   f zs = g (init $ tail $ inits zs) (tail $ init $ tails zs)

   g (xs:xss) (ys:yss)

     | h xs      = h ys || f ys || g xss yss

     | otherwise = g xss yss

     where h ds = head ds /= '0' && a010052 (read ds) == 1

   g _ _ = False

-- Reinhard Zumkeller, Oct 11 2011

CROSSREFS

Cf. A048646, A048375, A010052, A000290; subsequence of A128783.

Sequence in context: A274334 A083681 A178660 * A205807 A075696 A061120

Adjacent sequences:  A048650 A048651 A048652 * A048654 A048655 A048656

KEYWORD

base,nice,nonn

AUTHOR

Felice Russo

EXTENSIONS

Corrected and extended by Naohiro Nomoto, Sep 01 2001

STATUS

approved

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Last modified July 23 14:59 EDT 2017. Contains 289688 sequences.