A060610 Repeatedly apply Euler phi to the n-th prime; a(n) is the number of terms in the resulting iteration chain which are not powers of 2 (number of initial iterations until reaching the first power of 2).

0, 1, 1, 2, 2, 2, 1, 3, 3, 3, 2, 3, 2, 3, 4, 3, 4, 2, 3, 3, 3, 3, 3, 3, 2, 3, 2, 4, 4, 3, 4, 3, 2, 4, 4, 3, 3, 5, 4, 4, 4, 3, 4, 2, 4, 3, 3, 4, 4, 4, 4, 3, 2, 4, 1, 4, 4, 4, 4, 3, 5, 4, 3, 3, 3, 4, 3, 3, 5, 4, 3, 5, 3, 3, 5, 5, 3, 3, 3, 2, 4, 3, 4, 4, 4, 3, 3, 4, 4, 3, 5, 4, 6, 4, 4, 5, 5, 3, 4, 4, 4, 5, 4, 4, 4

Offset

1,4

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A049115(A000040(n)).

Example

n=100,p(100)=541, Phi-iteration chain is {541,540,144,48,16,8,4,2,1} with 9 terms. The first 4 terms (541,540,144,48) are not powers of 2, som a(100)=4.

Mathematica

Table[Count[FixedPointList[EulerPhi[#]&, Prime[n]], _?(!IntegerQ[ Log[ 2, #]]&)], {n, 110}] (* Harvey P. Dale, Sep 18 2016 *)

Crossrefs

Cf. A000040, A000010, A049108, A049113, A049116, A049115, A003434.

Sequence in context: A269400 A130267 A373687 * A352671 A351581 A017125

Adjacent sequences: A060607 A060608 A060609 * A060611 A060612 A060613

Keyword

easy,nonn

Author

Labos Elemer, Apr 13 2001

Extensions

Definition clarified by Harvey P. Dale, Sep 18 2016

Status

approved