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%I #22 Apr 18 2020 22:19:41
%S 1,3,5,15,25,73,125,365,625,1249,3125,6245,15625,31225,62497,156125,
%T 312485,780625,1560001,3903125,7800005,19515625,39000025,78000049,
%U 195000125,390000245,1948441249,3905875009,7811750017,19529375045
%N Position of first occurrence of n in A331410.
%C Conjecture: a(n) > a(n-1) and a(n) ~= sqrt(5)*a(n-1).
%C Often, a(n) = 5*a(n-2) as when n is 2, 3, 4, 6, 7, 8, 10, 11, 12, 13, 15, 16, 17, 19, 20, 21, 22, 24, 25, 29, ..., . [Corrected by _Jon E. Schoenfield_, Apr 05 2020]
%C The first occurrence of k at an even index is 2*a(k).
%e a(3) = 15 since A331410(15) = 3 and it is the first time 3 occurs. See the example in A331410.
%t a[n_] := -1 + Length@ NestWhileList[# + #/FactorInteger[#][[-1, 1]] &, n, # != 2^IntegerExponent[#, 2] &]; k = 1; t[_] := 0; While[k < 1000001, b = a@k; If[t[b] == 0, t[b] = k; Print[{b, k}]]; k+=2]; t@# & /@ Range[0, 17]
%Y Cf. A331410.
%K nonn
%O 0,2
%A _Ali Sada_ and _Robert G. Wilson v_, Feb 28 2020