A379854 a(0) = 0, and for any n > 0, a(n) is the least integer (in absolute value) not yet in the sequence such that the absolute difference of a(n-1) and a(n) is a cube; in case of a tie, preference is given to the positive value.

0, 1, 2, 3, 4, -4, -3, -2, -1, 7, 6, 5, 13, 12, 11, 10, 9, 8, 16, -11, -10, -9, -8, -7, -6, -5, -13, -12, 15, 14, 22, 21, 20, 19, 18, 17, 25, 24, 23, 31, 30, 29, 28, 27, 26, 34, -30, -22, -14, -15, -16, -17, -18, -19, -20, -21, -29, -28, -27, -26, -25, -24

Offset

0,3

Comments

A variant of A377091 based on cubes instead of squares.

Conjecture: Every integer (positive or negative) appears in this sequence.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Rémy Sigrist, PARI program

Example

The initial terms are:
  n   a(n)  |a(n)-a(n-1)|
  --  ----  -------------
   0     0  N/A
   1     1  1^3
   2     2  1^3
   3     3  1^3
   4     4  1^3
   5    -4  2^3
   6    -3  1^3
   7    -2  1^3
   8    -1  1^3
   9     7  2^3
  10     6  1^3
  11     5  1^3
  12    13  2^3
  13    12  1^3
  14    11  1^3

Prog

(PARI) \\ See Links section.
(Python)
from sympy import integer_nthroot
from itertools import count, islice
def cond(n): return integer_nthroot(n, 3)[1]
def agen(): # generator of terms
    an, aset, m = 0, {0}, 1
    for n in count(0):
        yield an
        an = next(s for k in count(m) for s in [k, -k] if s not in aset and cond(abs(an-s)))
        aset.add(an)
        while m in aset and -m in aset: m += 1
print(list(islice(agen(), 62))) # Michael S. Branicky, Jan 04 2025

Crossrefs

Cf. A377091.

Sequence in context: A301297 A167831 A090281 * A316823 A372982 A051951

Adjacent sequences: A379848 A379850 A379853 * A379855 A379856 A379858

Keyword

sign,new

Author

Rémy Sigrist, Jan 04 2025

Status

approved