A136041 Largest prime p such that phi^n(p) = 2, where phi^n means n iterations of Euler's totient function.

3, 7, 19, 43, 163, 487, 1459, 3079, 8803, 39367, 78787, 196831, 581743, 2125819, 6381667, 19131877, 86093443, 258280327, 516560659, 1214874127

Offset

1,1

Comments

The largest prime in row n+1 of A058812. From Shapiro, we know that a(n) <= 1 + 2*3^(n-1). This bound is attained for n=1,2,3,5,6,7,17,18,.., which is n=A003306(k)+1 for k=1,2,3,...

Links

Table of n, a(n) for n=1..20.

Harold Shapiro, An arithmetic function arising from the phi function, Amer. Math. Monthly, Vol. 50, No. 1 (1943), 18-30.

Mathematica

nn=20; pk=Table[0, {nn}]; Do[p=Prime[n]; k=Length[NestWhileList[EulerPhi, p, #>2&]]-1; If[0<k<=nn, pk[[k]]=p], {n, PrimePi[1+2*3^(nn-1)]}]; pk

Crossrefs

Sequence in context: A075900 A176500 A334099 * A146685 A146653 A096447

Adjacent sequences: A136038 A136039 A136040 * A136042 A136043 A136044

Keyword

nonn,more

Author

T. D. Noe, Dec 12 2007

Status

approved