A136041 - OEIS

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

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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