A066422 - OEIS

A066422

a(n) = least k such that phi^(k)(n) + 1 is prime, where phi^(k) denotes application of phi k times.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 1, 1, 2, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 3, 2, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 1, 2, 4, 3, 1, 3, 1, 1, 1, 1, 1, 3, 1, 2

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OFFSET

1,15

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

EXAMPLE

phi(phi(15)) + 1 = phi(8) + 1 = 4 + 1 = 5, a prime, so a(15) = 2.

MATHEMATICA

a[n_] := -1 + Length@ NestWhileList[EulerPhi, n, ! PrimeQ[# + 1] &, {2, 1}]; Array[a, 80] (* Amiram Eldar, Nov 10 2024 *)

PROG

(PARI) a(n) = {nb = 1; n = eulerphi(n); while(! isprime(n+1), n = eulerphi(n); nb ++; ); return (nb); } \\ Michel Marcus, May 18 2013

CROSSREFS

Cf. A000010.

Sequence in context: A140500 A156054 A030616 * A274888 A239702 A378399

Adjacent sequences: A066419 A066420 A066421 * A066423 A066424 A066425

KEYWORD

nonn

AUTHOR

Joseph L. Pe, Dec 26 2001

EXTENSIONS

Corrected and extended by Michel Marcus, May 18 2013

STATUS

approved