OFFSET
1,2
COMMENTS
The graph appears to have a shape similar to that of Mertens function A002321, with increasingly large "mountains" and "valleys":
Successive record values of opposite sign are a(2) = 2, a(3) = -1, a(5) = 10, a(10) = -85, a(16) = 186, a(222) = -75573, a(391) = 26186, a(658) = -341791, a(987) = 134304, a(1831) = -1820815, a(2476) = 393048, a(2692) = -2089141, a(3321) = 1816290, a(6114) = -8650189, ...
LINKS
M. F. Hasler, Table of n, a(n) for n = 1..10000
Eric Angelini, Re: Add or subtract my cumulative sum of digits, SeqFan list, Feb 24 2020.
EXAMPLE
a(1) = 1 is odd, so we add the partial sum (so far equal to a(1)) to get the next term, a(2) = 2.
Now a(2) = 2 is even, so we subtract the sum of the digits of a(1) and a(2), 1 + 2 = 3 to get a(3) = -1.
Since a(3) = -1 is odd, we add the sum of the digits of a(1), a(2) and a(3), 1 + 2 + 1 = 4 to get a(4) = 3.
And so on.
MATHEMATICA
Nest[Append[#, #[[-1]] + (2 Boole[OddQ@ #[[-1]] ] - 1)*Total[Flatten@ IntegerDigits[#]] ] &, {1}, 41] (* Michael De Vlieger, Feb 25 2020 *)
PROG
(PARI) A332058_vec(N, a=1, s=-a)={vector(N, n, a-=(-1)^a*s+=sumdigits(a))}
CROSSREFS
KEYWORD
sign,base
AUTHOR
Eric Angelini and M. F. Hasler, Feb 24 2020
STATUS
approved