A354731 Absolute values of first differences of A354688.

1, 3, 2, 4, 5, 7, 15, 9, 8, 13, 17, 19, 11, 6, 12, 14, 20, 10, 29, 21, 16, 22, 23, 27, 25, 31, 18, 47, 35, 33, 37, 26, 61, 39, 34, 28, 24, 55, 43, 41, 45, 38, 40, 30, 32, 44, 89, 59, 57, 49, 53, 65, 58, 51, 63, 115, 67, 56, 46, 36, 91, 71, 69, 73, 62, 48, 42, 99, 77, 50, 125, 79, 75, 83, 85, 81

Offset

1,2

Comments

See A354688 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 10000. The green line is y = n.

Example

a(3) = 2 as | A354688(4) - A354688(3) | = | 3 - 5 | = 2.

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}, set(), 1, 2
    for n in count(2):
        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(k-an); an = k
        while mink in aset: mink += 1
print(list(islice(agen(), 76))) # Michael S. Branicky, Jun 04 2022

Crossrefs

Cf. A354688, A352588, A093714, A354687, A354721.

Sequence in context: A039882 A370803 A326357 * A164287 A086962 A001612

Adjacent sequences: A354728 A354729 A354730 * A354732 A354733 A354734

Keyword

nonn

Author

Scott R. Shannon, Jun 04 2022

Status

approved