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

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, -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, 5, -2, 0, -7, 4, 6, 8, -8, -6, 5, 7, -9, 2, -5, -3, 8, 1, 3, -4

Offset: 1

Author

Reinhard Zumkeller, Apr 12 2014

Keywords

• sign
• base

Links

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

Crossrefs

Cf. A004159, A000290, A007953.

Cf. A202089, A239878, A240754.

Programs

Haskell

a240752 n = a240752_list !! (n-1)
a240752_list = zipWith (-) (tail a004159_list) a004159_list

Mathematica

Differences[Total[IntegerDigits[#]]&/@(Range[0,80]^2)] (* Harvey P. Dale, Mar 10 2019 *)

PARI

a(n) = sumdigits(n^2) - sumdigits((n-1)^2); \\ Michel Marcus, Jan 24 2022

Python

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

Formula

a(n) = A004159(n) - A004159(n-1).

a(n) = A007953(A000290(n)) - A007953(A000290(n-1)).

a(A202089(n)+1) = 0; a(A239878(n)+1) = 1; a(A240754(n)+1) = -1.

Extensions

Formulas adapted to offset by Michel Marcus, Jan 25 2022