A377388 Infinite sequence of integers a(1), a(2), ... such that for any n > 0, a(n) is as small as possible (in absolute value) and the means of consecutive terms are all distinct; in case of a tie, preference is given to the positive value.

0, 1, -2, -3, -5, -8, -6, -11, -13, -21, -16, 9, -42, -24, -25, -27, -34, -35, -46, 10, 2, 90, 42, 31, 26, 11, 30, 18, 58, 41, 20, 86, 43, 60, 45, 103, 48, 54, 105, 83, -48, -151, -155, -59, -87, -79, -146, 106, -157, -109, -218, -208, -88, -45, -99, -131, 27

Offset

1,3

Comments

This sequence is a variant of A377351 allowing negative values.

All terms are distinct.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, C++ program

Example

The first terms, alongside the means of consecutive terms ending with a(n), are:
  n  a(n)  Corresponding means
  -  ----  -----------------------------------------
  1     0  0
  2     1  1/2, 1
  3    -2  -1/3, -1/2, -2
  4    -3  -1, -4/3, -5/2, -3
  5    -5  -9/5, -9/4, -10/3, -4, -5
  6    -8  -17/6, -17/5, -9/2, -16/3, -13/2, -8
  7    -6  -23/7, -23/6, -24/5, -11/2, -19/3, -7, -6

Prog

(C++) // See Links section.
(Python)
from fractions import Fraction
from itertools import count, islice
def A377388gen(): # generator of terms
    alst, means_seen = [0], {0}
    while True:
        yield alst[-1]
        for i in count(1):
            failed = True
            for k in [i, -i]:
                if k in means_seen: continue
                mk, failed, sk = {k}, False, k
                for j in range(1, len(alst)+1):
                    sk += alst[-j]
                    m = Fraction(sk, j+1)
                    if m in means_seen or m in mk: failed = True; break
                    mk.add(m)
                if not failed:
                    means_seen |= mk
                    alst.append(k)
                    break
            if not failed: break
print(list(islice(A377388gen(), 60))) # Michael S. Branicky, Oct 27 2024, Oct 28 2024

Crossrefs

Cf. A377351, A377389.

Sequence in context: A262263 A072987 A010075 * A182445 A010074 A355702

Adjacent sequences: A377385 A377386 A377387 * A377389 A377390 A377391

Keyword

sign

Author

Rémy Sigrist, Oct 27 2024

Status

approved