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%I #13 Apr 15 2023 15:02:34
%S 3,7,23,71,311,461,799,1271,719,941,967,1151,1783,1847,2659,1621,3067,
%T 1663,3583,2467,2851,2551,4051,5741,6239,6373,6271,5927,8627,6841,
%U 5603,4201,5581,9901,6037,8423,7487,7123,5867,5791,6011,8539,13119,6367,13327,11863
%N Position of the first occurrence of n in sequence A196942.
%C a(n) is also the smallest positive integer such that the prime number order of p3 has to be n or larger when a(n) is written as a(n) = p1^m1 * p2^m2 * p3^m3 + p1^n1 * p2^n2 * p3^n3, where p1 < p2 < p3 are prime numbers and m1,m2,m3 and n1,n2,n3 are integers greater than or equal to zero.
%H Lei Zhou, <a href="/A225914/b225914.txt">Table of n, a(n) for n = 1..186</a>
%e 1 appears first at position 3 in A196942, so a(1)=3;
%e 3 appears first at position 23 in A196942, so a(3)=23.
%t max = 46; res = Table[0, {i, 1, max}]; i = 1; ct = 0; While[ct < max, i++; ref = i; Do[k = i - j; fj = Transpose[FactorInteger[j]][[1]]; fk = Transpose[FactorInteger[k]][[1]]; fpls = Union[fj, fk]; lf = Length[fpls]; If[lf <= 3, cd = fpls[[lf]]; If[cd < ref, ref = cd]], {j,Ceiling[i/2], i}]; tag = PrimePi[ref]; If[tag <= max, If[res[[tag]] == 0, res[[tag]] = i; ct++]]]; res
%Y Cf. A000040, A196491, A196492.
%K nonn
%O 1,1
%A _Lei Zhou_, May 20 2013
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