A078589 a(1)=0, a(2)=1, a(n) = abs(abs(a(n-1)) - a(n-2) - n + 1).

0, 1, 1, 3, 2, 6, 2, 11, 1, 19, 8, 22, 2, 33, 17, 31, 2, 46, 26, 39, 7, 53, 24, 52, 4, 73, 43, 57, 14, 72, 28, 75, 15, 93, 44, 84, 4, 117, 75, 81, 34, 88, 12, 119, 63, 101, 8, 140, 84, 105, 29, 127, 46, 134, 34, 155, 65, 147, 24, 182, 98, 145, 15, 193, 114, 144, 36, 175

Offset

1,4

Comments

It seems that lim_{n -> oo} M(n)/n = 3.4... where M(n) = Max(a(k), 1<=k<=n). Does a(n)=1 for a finite number of values? The first ones are 2, 3, 9, 177, 3891, ...

The next one (where a(n)=1) is 205653 and there are no further instances up to a(5 million). - Harvey P. Dale, Dec 13 2025

Links

John Tyler Rascoe, Table of n, a(n) for n = 1..10000

Mathematica

nxt[{n_, a_, b_}]:={n+1, b, Abs[Abs[b]-a-n]}; NestList[nxt, {2, 0, 1}, 70][[;; , 2]] (* Harvey P. Dale, Dec 13 2025 *)

Prog

(Python)
def A078589_list(max_n):
    A = [0, 1]
    for n in range(3, max_n + 1):
        A.append(abs(A[-1] - A[-2] - n + 1))
    return(A) # John Tyler Rascoe, Oct 25 2022

Crossrefs

Sequence in context: A180240 A065228 A092843 * A077880 A198930 A389793

Adjacent sequences: A078586 A078587 A078588 * A078590 A078591 A078592

Keyword

nonn

Author

Benoit Cloitre, Dec 06 2002

Status

approved