OFFSET
1,2
COMMENTS
The instructions of this two-register counting machine are to be interpreted as follows: Two registers are initialized to zero, and the instruction pointer starts on the first instruction. i[k] means increment the k-th register. The instruction pointer then moves to the next instruction. d[k,l] means decrement the k-th register if it is nonzero, and then change the instruction pointer to l. Otherwise move the instruction pointer to the next instruction. The following set of 8 instructions is given in the book 'A New Kind of Science' by Stephen Wolfram as one of the simplest register machines which has complex behavior: {i[1], i[1], i[1], d[2,1], d[1,6], i[2], d[1,5], d[2,3]}. This sequence distills information about the states of the register machine by including only the values of the first register, at those times when the 2nd register has just been decremented to zero.
REFERENCES
Wolfram, S., A New Kind of Science. Champaign, IL: Wolfram Media, pp. 97-102, 2002.
FORMULA
It appears that a(n) = A070885(n+1) - 2. - Luc Rousseau, Jun 08 2017
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jack W Grahl, Feb 11 2009
EXTENSIONS
Rousseau's suggested formula verified by Glen Whitney, Aug 03 2018
STATUS
approved