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

2, 4, 15, 33, 90, 129, 227, 288, 429, 694, 798, 1149, 1417, 1565, 1879, 2399, 2993, 3201, 3879, 4365, 4623, 5429, 6002, 6920, 8245, 8948, 9314, 10067, 10457, 11245, 14251, 15184, 16627, 17130, 19711, 20253, 21919, 23653, 24845, 26687, 28604, 29248, 32612, 33303, 34719, 35436, 39893, 44622, 46254

Offset

1,1

Links

Table of n, a(n) for n=1..49.

Formula

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

Example

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!

Mathematica

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
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 *)

Crossrefs

Cf. A045763, A073759, A002808, A073813.

Cf. A120389. [From R. J. Mathar, Aug 07 2008]

Sequence in context: A260299 A080623 A196260 * A181442 A007122 A005219

Adjacent sequences: A073811 A073812 A073813 * A073815 A073816 A073817

Keyword

nonn

Author

Labos Elemer, Aug 15 2002

Extensions

Definition corrected by Gionata Neri, Mar 28 2016

More terms from Michael De Vlieger, Mar 28 2016

Status

approved