A072927 a(n) = minimum value of abs(n-phi(x)), x>0.

0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 3, 2, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0

Offset

1,14

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Sean A. Irvine)

Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Amiram Eldar, Plot of Sum_{k=1..n} a(k)/(n*log(n)) for n = 2^(1..26).

Formula

a(A002202(n)) = 0.

It seems that Sum_{k=1..n} a(k) is asymptotic to C*n*log(n) with C = 0.15... .

Prog

(PARI) a(n) = if(invphiNum(n) > 0, return(0)); for(k = 1, n-1, forstep(isign = -1, 1, 2, if(invphiNum(n + isign*k) > 0, return(k)))); \\ Amiram Eldar, Apr 18 2025, using Max Alekseyev's invphi.gp (see links).

Crossrefs

Cf. A000010, A002202.

Sequence in context: A123737 A083037 A247477 * A307194 A331218 A120086

Adjacent sequences: A072924 A072925 A072926 * A072928 A072929 A072930

Keyword

easy,nonn

Author

Benoit Cloitre, Aug 11 2002

Status

approved