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A354731
Absolute values of first differences of A354688.
4
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
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
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Jun 04 2022
STATUS
approved