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

Author

Rémy Sigrist, Sep 01 2025

Keywords

• nonn
• new

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A386482.

Programs

PARI

\\ See Links section.