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

Author

T. D. Noe, Dec 12 2007

Keywords

• nonn
• more

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

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

Programs

Mathematica

nn=20; pk=Table[0,{nn}]; Do[p=Prime[n]; k=Length[NestWhileList[EulerPhi,p,#>2&]]-1; If[0