A175079 - OEIS

%I #6 Aug 04 2022 05:53:07

%S 1,3,10,123,1357324

%N The smallest natural numbers m with first occurrence 0, 1, 2, 3, ... for number of steps of iterations of {r mod (max prime p < r)} needed to reach 1 or 2 starting at r = m.

%C I offer a prize of 100 liters of Pilsner Urquell to the discoverer of a(5). Conjecture: a(n) is not equal A135543(n) + 1 for all n >= 1. See A175071 (natural numbers m with result 1) and A175072 (natural numbers m with result 2). See A175077 (results 1 or 2 under iterations) and A175078 (number of steps of iterations).

%F From _Pontus von Brömssen_, Jul 31 2022: (Start)

%F a(n) = A135543(n) + 1 for n >= 1, i.e., the conjecture in the Comments is false. This follows from the result that A175078(n) = A121561(n-1) for n >= 2.

%F a(5) = A135543(5) + 1 <= A002110(8787)/510510 + 291362 (see comment in A135543).

%F (End)

%e Iteration for a(4) = 1357324 has 4 steps: 1357324 mod 1357201 = 123, 123 mod 113 = 10, 10 mod 7 = 3, 3 mod 2 = 1.

%Y Cf. A002110, A121561, A135543, A175071, A175072, A175077, A175078.

%K nonn,more

%O 0,2

%A _Jaroslav Krizek_, Jan 23 2010

%E _Jaroslav Krizek_, Jan 30 2010