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Search: id:A136041
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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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1
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| 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
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1,1
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COMMENT
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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
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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
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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
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Sequence in context: A055622 A075900 A069051 this_sequence A146685 A146653 A096447
Adjacent sequences: A136038 A136039 A136040 this_sequence A136042 A136043 A136044
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Dec 12 2007
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