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.

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, 22, 9, 5, 19, 10, 35, 31, 31, 60, 47, 33, 44, 46, 15, 8, 49, 14, 9, 12, 23, 35, 34, 28, 11, 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

Offset

0,1

Comments

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.

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.

Links

Table of n, a(n) for n=0..77.

Example

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.
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.
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.

Crossrefs

Cf. A352406 (addition), A079777.

Sequence in context: A287139 A288770 A249826 * A364037 A321226 A337329

Adjacent sequences: A352404 A352405 A352406 * A352408 A352409 A352410

Keyword

nonn

Author

Scott R. Shannon, Mar 15 2022

Status

approved