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A136041
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Largest prime p such that phi^n(p) = 2, where phi^n means n iterations of Euler's totient function.
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0
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3, 7, 19, 43, 163, 487, 1459, 3079, 8803, 39367, 78787, 196831, 581743, 2125819, 6381667, 19131877, 86093443, 258280327, 516560659, 1214874127
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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,...
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REFERENCES
| Harold Shapiro, An arithmetic function arising from the phi function, Amer. Math. Monthly, Vol. 50, No. 1 (1943), 18-30.
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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
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CROSSREFS
| Sequence in context: A075900 A176500 A069051 * A146685 A146653 A096447
Adjacent sequences: A136038 A136039 A136040 * A136042 A136043 A136044
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KEYWORD
| nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Dec 12 2007
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