

A332058


a(1) = 1; a(n+1) = a(n) + (sum of digits of a(1) up to a(n)), with "+" when a(n) is odd, or "" if even.


2



1, 2, 1, 3, 10, 2, 8, 26, 52, 85, 39, 19, 87, 170, 79, 186, 64, 68, 214, 367, 198, 385, 182, 396, 628, 876, 1145, 865, 566, 882, 1216, 1560, 1916, 2289, 1895, 1478, 1915, 1462, 1928, 2414, 2911, 2401
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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

See A332056 for the variant considering sum of a(n) instead of digits.
Sequence in context: A246063 A332064 A229417 * A260758 A091858 A070165
Adjacent sequences: A332055 A332056 A332057 * A332059 A332060 A332061


KEYWORD

sign,base


AUTHOR

Eric Angelini and M. F. Hasler, Feb 24 2020


STATUS

approved



