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a(n) is the prime order of sequence A196941.
1

%I #15 Mar 14 2015 00:41:16

%S 0,1,1,1,1,2,1,1,1,2,1,2,2,2,1,1,1,2,1,2,2,3,1,2,2,2,2,2,2,2,1,1,1,2,

%T 1,2,2,2,1,2,2,2,2,2,3,3,1,2,2,2,2,3,2,2,2,2,2,2,2,3,2,2,1,1,1,2,1,3,

%U 2,4,1,2,2,2,2,3,2,3,1,2,2,2,2,2,2,2,2

%N a(n) is the prime order of sequence A196941.

%C Assuming 1 is the 0th prime, as what in Mathematica: PrimePi[1] = 0.

%C So far the first occurrence of this sequence agree with A062241 and A045535. Is this a coincidence or a theorem?

%e A196941(3) = 2, which is the first prime number, so a(3) = 1;

%t FactorSet[seed_] := Module[{fset2, a, l, i}, a = FactorInteger[seed]; l = Length[a]; fset2 = {}; Do[fset2 = Union[fset2, {a[[i]][[1]]}], {i, 1, l}]; fset2]; Table[min = n; Do[r = n - k; s = Union[FactorSet[k], FactorSet[r]]; If[a = s[[Length[s]]]; a < min, min = a], {k, 1, IntegerPart[n/2]}]; PrimePi[min], {n, 2, 88}]

%Y Cf. A196941, A062241.

%K nonn,easy

%O 2,6

%A _Lei Zhou_, Oct 07 2011