This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A352407 #11 Mar 19 2022 09:43:15 %S A352407 2,3,14,5,5,11,4,42,54,6,17,38,6,27,12,71,20,5,6,8,12,12,42,37,36,23, %T A352407 22,9,5,19,10,35,31,31,60,47,33,44,46,15,8,49,14,9,12,23,35,34,28,11, %U A352407 86,43,20,49,18,17,12,9,22,45,26,5,31,51,72,7,6,121,120,111,86,341,56,63,12,85,12,21 %N A352407 The number of terms before reaching zero when starting at n and iterating: f(n) = n, f(n+1) = n+1; f(n+k) = (f(n+k-2) * f(n+k-1)) (mod (n+k)), where k>=2. %C A352407 This sequences uses the same iterative formula as A352406 except that the two previous terms are multiplied instead of added. See that sequence for further details. %C A352407 In the first 500000 terms the largest value is a(409758) = 1480452. In the same range the smallest number greater than 1 not to have appeared is 16291, although it is likely all numbers eventually appear. %e A352407 a(0) = 2 as starting at 0 and 1 gives 0*1 % 2 = 0, with two terms before reaching zero. This is the smallest possible value and the only term to equal 2. %e A352407 a(2) = 14 as starting at 2 and 3 gives 2*3 % 4 = 2, 3*2 % 5 = 1, 2*1 % 6 = 2, 1*2 % 7 = 2, 2*2 % 8 = 4, 2*4 % 9 = 8, 4*8 % 10 = 2, 8*2 % 11 = 5, 2*5 % 12 = 10, 5*10 % 13 = 11, 10*11 % 14 = 12, 11*12 % 15 = 12, 12*12 % 16 = 0, with fourteen terms before reaching zero. %e A352407 a(3) = 5 as starting at 3 and 4 gives 3*4 % 5 = 2, 4*2 % 6 = 2, 2*2 % 7 = 4, 2*4 % 8 = 0, with five terms before reaching zero. %Y A352407 Cf. A352406 (addition), A079777. %K A352407 nonn %O A352407 0,1 %A A352407 _Scott R. Shannon_, Mar 15 2022