A387542 a(n) is the distance from the n-th term of A386482 to the nearest term of A386482 coprime to it.

0, 1, 2, 3, 2, 2, 4, 2, 2, 4, 2, 2, 2, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 4, 2, 2, 2, 2, 3, 5, 4, 3, 5, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 4, 2, 2, 2, 2, 3, 5, 5, 6, 5, 4, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 5, 6, 8, 8, 9, 11

Offset

1,3

Comments

In other words: a(n) is the least d >= 0 such that gcd(A386482(n), A386482(n - d)) = 1 or gcd(A386482(n), A386482(n + d)) = 1.

The sequence is well defined as A386482(1) = 1 is coprime to all terms of A386482.

Links

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

Rémy Sigrist, PARI program

Example

For n = 7: the GCD of A386482(7) = 12 and its neighboring terms are:
  d   A387542(7+d)  gcd(A387542(7), A387542(7+d))
  --  ------------  -----------------------------
  -4             4                              4
  -3             6                              6
  -2             3                              3
  -1             9                              3
   0            12                             12
   1            10                              2
   2             8                              4
   3            14                              2
   4             7                              1
The nearest coprime term, A387542(11) = 7, is at distance 4, so a(7) = 4.

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A386482.

Sequence in context: A368713 A375341 A368039 * A382969 A393085 A160558

Adjacent sequences: A387539 A387540 A387541 * A387543 A387544 A387545

Keyword

nonn

Author

Rémy Sigrist, Sep 01 2025

Status

approved