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A240752 First differences of digit sums of squares, cf. A004159.

%I A240752 #18 Mar 15 2023 17:04:56
%S A240752 1,3,5,-2,0,2,4,-3,-1,-8,3,5,7,0,-7,4,6,-10,1,-6,5,7,0,2,-5,6,-1,1,-6,
%T A240752 -4,7,-9,11,-5,-3,8,1,-6,-4,-2,9,2,4,-3,-10,1,3,-4,-2,0,2,4,6,-1,-8,3,
%U A240752 5,-2,0,-7,4,6,8,-8,-6,5,7,-9,2,-5,-3,8,1,3,-4
%N A240752 First differences of digit sums of squares, cf. A004159.
%H A240752 Reinhard Zumkeller, <a href="/A240752/b240752.txt">Table of n, a(n) for n = 1..10000</a>
%F A240752 a(n) = A004159(n) - A004159(n-1).
%F A240752 a(n) = A007953(A000290(n)) - A007953(A000290(n-1)).
%F A240752 a(A202089(n)+1) = 0; a(A239878(n)+1) = 1; a(A240754(n)+1) = -1.
%t A240752 Differences[Total[IntegerDigits[#]]&/@(Range[0,80]^2)] (* _Harvey P. Dale_, Mar 10 2019 *)
%o A240752 (Haskell)
%o A240752 a240752 n = a240752_list !! (n-1)
%o A240752 a240752_list = zipWith (-) (tail a004159_list) a004159_list
%o A240752 (PARI) a(n) = sumdigits(n^2) - sumdigits((n-1)^2); \\ _Michel Marcus_, Jan 24 2022
%o A240752 (Python)
%o A240752 def A240752(n): return sum(map(int,str(m:=n**2)))-sum(map(int,str(m-(n<<1)+1))) # _Chai Wah Wu_, Mar 15 2023
%Y A240752 Cf. A004159, A000290, A007953.
%Y A240752 Cf. A202089, A239878, A240754.
%K A240752 sign,base
%O A240752 1,2
%A A240752 _Reinhard Zumkeller_, Apr 12 2014
%E A240752 Formulas adapted to offset by _Michel Marcus_, Jan 25 2022