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 A048653 Numbers k such that the decimal digits of k^2 can be partitioned into two or more nonzero squares. 4
 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-François 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 (Python) from math import isqrt def issquare(n): return isqrt(n)**2 == n def ok(n, c):     if n%10 in {2, 3, 7, 8}: return False     if issquare(n) and c > 1: return True     d = str(n)     for i in range(1, len(d)):         if d[i] != '0' and issquare(int(d[:i])) and ok(int(d[i:]), c+1):             return True     return False def aupto(lim): return [r for r in range(lim+1) if ok(r*r, 1)] print(aupto(650)) # Michael S. Branicky, Jul 10 2021 CROSSREFS Cf. A048646, A048375, A010052, A000290; subsequence of A128783. Sequence in context: A328414 A083681 A178660 * A205807 A075696 A061120 Adjacent sequences:  A048650 A048651 A048652 * A048654 A048655 A048656 KEYWORD base,nice,nonn AUTHOR EXTENSIONS Corrected and extended by Naohiro Nomoto, Sep 01 2001 Definition clarified by Harvey P. Dale, May 09 2021 STATUS approved

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Last modified July 6 22:19 EDT 2022. Contains 355115 sequences. (Running on oeis4.)