A354721 Absolute values of first differences of A354687.

1, 2, 4, 6, 8, 3, 9, 10, 12, 5, 15, 14, 18, 16, 20, 39, 13, 22, 33, 21, 27, 24, 11, 26, 28, 23, 46, 48, 7, 30, 34, 32, 49, 35, 36, 51, 45, 42, 25, 44, 55, 38, 66, 19, 57, 40, 87, 58, 54, 102, 52, 56, 50, 68, 85, 62, 60, 75, 65, 63, 108, 69, 64, 70, 72, 141, 17, 74, 88, 76, 78, 148, 80, 91, 77, 81

Offset

1,2

Comments

See A354687 for further details.

Links

Table of n, a(n) for n=1..76.

Michael De Vlieger, Annotated log log scatterplot of a(n), n = 1..2^14, showing records in red and local minima in blue, highlighting primes in green and fixed points in gold.

Scott R. Shannon, Image of the first 100000 terms. The green line is y = n.

Example

a(5) = 8 as | A354687(6) - A354687(5) | = | 6 - 14 | = 8.

Mathematica

nn = 120; c[_] = d[_] = 0; a[1] = c[1] = 1; a[2] = c[2] = j = 2; u = 3; {1}~Join~Reap[Do[Set[k, u]; While[Nand[c[k] == 0, d[Abs[k - j]] == 0, ! CoprimeQ[j, k]], k++]; Set[{a[i], c[k], d[Abs[k - j]]}, {k, i, i}]; Sow[Abs[k - j]]; j = k; If[k == u, While[c[u] > 0, u++]], {i, 3, nn}]][[-1, -1]] (* Michael De Vlieger, Jun 04 2022 *)

Prog

(Python)
from math import gcd
from sympy import isprime, nextprime
from itertools import count, islice
def agen(): # generator of terms
    aset, diffset, an, mink = {1, 2}, {1}, 2, 3
    yield from [1]
    for n in count(3):
        k = mink
        while k in aset or abs(an-k) in diffset or gcd(an, k) == 1: k += 1
        aset.add(k); diffset.add(abs(k-an)); yield abs(an-k); an = k
        while mink in aset: mink += 1
print(list(islice(agen(), 76))) # Michael S. Branicky, Jun 04 2022

Crossrefs

Cf. A354687, A064413, A354688, A354731, A354087, A352763.

Sequence in context: A308080 A179657 A239887 * A355506 A241012 A355213

Adjacent sequences: A354718 A354719 A354720 * A354722 A354723 A354724

Keyword

nonn

Author

Scott R. Shannon, Jun 04 2022

Status

approved