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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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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
KEYWORD
nonn,less
AUTHOR
Joseph L. Pe, Jan 18 2002
EXTENSIONS
More terms from Jinyuan Wang, Jul 30 2020
STATUS
approved

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)