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A073814 a(n) is the smallest number k such that A073813(k) = prime(n). 0

%I

%S 2,4,15,33,90,129,227,288,429,694,798,1149,1417,1565,1879,2399,2993,

%T 3201,3879,4365,4623,5429,6002,6920,8245,8948,9314,10067,10457,11245,

%U 14251,15184,16627,17130,19711,20253,21919,23653,24845,26687,28604,29248,32612,33303,34719,35436,39893,44622,46254

%N a(n) is the smallest number k such that A073813(k) = prime(n).

%F Min{x; c[x]-Max[URS[c[x]]]=p(n)}, p(n)=n-th prime. See program.

%e a(6)=129 means that c[129]-Max[URS[c[129]]=Prime[6]: c[129]=169, Max[URS[169]]=Max{26,39,...,143,156}=156; difference=169-156=13=6th prime. Suspicion: A073813(n) is always prime number!

%t c[x_] := FixedPoint[x+PrimePi[ # ]+1&, x]; tn[x_] := Table[j, {j, 1, x}]; di[x_] := Divisors[x]; rrs[x_] := Flatten[Position[GCD[tn[x], x], 1]]; rs[x_] := Union[rrs[x], di[x]]; urs[x_] := Complement[tn[x], rs[x]]; Do[s=c[n]-Max[urs[c[n]]]; If[s<101&&t[[s]]==0, t[[s]]=n], {n, 1, 10}]; t

%t nn = 6 * 10^4; s = Function[k, k - SelectFirst[Range[k - 2, 2, -1], 1 < GCD[#, k] < # &]] /@ Select[Range[6, nn], ! PrimeQ@ # &]; Table[SelectFirst[Range@ Length@ s, s[[# - 1]] == Prime@ n &], {n, 49}] (* _Michael De Vlieger_, Mar 28 2016, Version 10 *)

%Y Cf. A045763, A073759, A002808, A073813.

%Y Cf. A120389. [From _R. J. Mathar_, Aug 07 2008]

%K nonn

%O 1,1

%A _Labos Elemer_, Aug 15 2002

%E Definition corrected by _Gionata Neri_, Mar 28 2016

%E More terms from _Michael De Vlieger_, Mar 28 2016

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Last modified May 7 08:34 EDT 2021. Contains 343636 sequences. (Running on oeis4.)