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 A055616 Numbers, with an even number of digits, that are the sum of the squares of their two halves (leading zeros allowed only for the second half). 10
 1233, 8833, 990100, 94122353, 1765038125, 2584043776, 7416043776, 8235038125, 9901009901, 116788321168, 123288328768, 876712328768, 883212321168, 999900010000, 13793103448276, 15348303604525, 84651703604525, 86206903448276, 91103202846976, 92318202663025 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sequence is infinite since it contains several infinite subsequences (see A055617, etc.). If x = A*10^n+B is an element not beginning with 9, then (10^n-A)*10^n+B is another (e.g. 1233 <-> 8833). Numbers that can be written as n = A*10^d + B with 10^(d-1) <= A < 10^d, 0 <= B < 10^d, and A^2 + B^2 = n. - Robert Israel, May 10 2015 LINKS Robert Israel, Table of n, a(n) for n = 1..1000 EXAMPLE 8833 is ok, since 8833 = 88^2 + 33^2. MAPLE dmax:= 8: # to get all entries with at most 2*dmax digits Res:= NULL: for d from 2 to dmax  do      cands:= map(t -> subs(t, [x, y]), [isolve(x^2 + y^2 = 10^(2*d)+1)]);      cands:= select(t -> t[1]::even and t[1]>=0 and t[2]>0, cands);      cands:= map(t -> ([(10^d + t[1])/2, (t[2]+1)/2], [(10^d-t[1])/2, (t[2]+1)/2]), cands);      cands:= select(t -> (t[1]>= 10^(d-1) and t[1] < 10^d and t[2] <= 10^d), cands);      Res:= Res, op(map(t -> 10^d*t[1]+t[2], cands)); od: sort([Res]); # Robert Israel, May 10 2015 MATHEMATICA fQ[n_] := Block[{d = IntegerDigits@ n}, If[OddQ[Length@ d], False, Plus[FromDigits[Take[d, Length[d]/2]]^2, FromDigits[Take[d, -Length[d]/2]]^2]] == n]; Select[Range@ 1000000, fQ] (* Michael De Vlieger, May 09 2015 *) PROG (Python) def a(): ..n = 1 ..while n < 10**6: ....st = str(n) ....if len(st) % 2 == 0: ......s1 = st[:int(len(st)/2)] ......s2 = st[int(len(st)/2):int(len(st))] ......if int(s1)**2+int(s2)**2 == int(st): ........print(n, end=', ') ........n += 1 ......else: ........n += 1 ....else: ......n = 10*n a() # Derek Orr, Jul 08 2014 CROSSREFS Cf. A064942 for the number of solutions, where leading zeros are allowed. Cf. A055617, A055618, A055619. Sequence in context: A206272 A064942 A101311 * A104971 A193492 A279204 Adjacent sequences:  A055613 A055614 A055615 * A055617 A055618 A055619 KEYWORD nonn,base AUTHOR Ulrich Schimke (ulrschimke(AT)aol.com) EXTENSIONS Definition corrected by Derek Orr, Jul 09 2014 STATUS approved

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Last modified January 24 00:58 EST 2019. Contains 319404 sequences. (Running on oeis4.)