A329662 Position of first occurrence of n in A331410.

1, 3, 5, 15, 25, 73, 125, 365, 625, 1249, 3125, 6245, 15625, 31225, 62497, 156125, 312485, 780625, 1560001, 3903125, 7800005, 19515625, 39000025, 78000049, 195000125, 390000245, 1948441249, 3905875009, 7811750017, 19529375045

Offset: 0

Author

Ali Sada and Robert G. Wilson v, Feb 28 2020

Keywords

• nonn

Comments

Conjecture: a(n) > a(n-1) and a(n) ~= sqrt(5)*a(n-1).

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]

The first occurrence of k at an even index is 2*a(k).

Examples

			a(3) = 15 since A331410(15) = 3 and it is the first time 3 occurs. See the example in A331410.
		

Crossrefs

Cf. A331410.

Programs

Mathematica

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]