A066786 a(n) is the least k such that the distance between (n, phi(n)) and (n+k, phi(n+k)) is an integer (i.e., k^2 + (phi(n+k) - phi(n))^2 is a square), or 0 if none exists.

1, 12, 1, 2, 3, 3, 2, 2, 5, 2, 3, 3, 3, 4, 1, 4, 15, 8, 8, 4, 3, 48, 23, 6, 5, 2, 8, 8, 5, 24, 8, 2, 11, 6, 4, 6, 20, 16, 6, 8, 7, 32, 6, 6, 6, 33, 8, 7, 8, 16, 13, 4, 15, 25, 16, 14, 6, 27, 35, 33, 16, 8, 6, 4, 7, 105, 67, 12, 15, 2, 71, 6, 18, 2, 7, 15, 16, 6

Offset

1,2

Links

Table of n, a(n) for n=1..78.

Example

12^2 + (phi(2+12) - phi(2))^2 = 13^2 and k = 12 is the least natural number achieving this, so a(2) = 12.

Prog

(PARI) a(n) = for(k=1, oo, if(issquare(k^2 + (eulerphi(n+k) - eulerphi(n))^2), return(k))); \\ Jinyuan Wang, Jul 30 2020

Crossrefs

Cf. A000010.

Sequence in context: A289673 A010211 A335503 * A109015 A010210 A361206

Adjacent sequences: A066783 A066784 A066785 * A066787 A066788 A066789

Keyword

nonn,less

Author

Joseph L. Pe, Jan 18 2002

Extensions

More terms from Jinyuan Wang, Jul 30 2020

Status

approved