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A156622 Values of register a when register b becomes 0 for the two-register machine {i[1], i[1], i[1], d[2,1], d[1,6], i[2], d[1,5], d[2,3]}. 1
1, 4, 7, 13, 22, 34, 52, 79, 121, 184, 277, 418, 628, 943, 1417, 2128, 3193, 4792, 7189, 10786, 16180, 24271, 36409, 54616, 81925, 122890, 184336 (list; graph; refs; listen; history; text; internal format)



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.


Wolfram, S., A New Kind of Science. Champaign, IL: Wolfram Media, pp. 97-102, 2002.


Table of n, a(n) for n=1..27.


It appears that a(n) = A070885(n+1) - 2. - Luc Rousseau, Jun 08 2017

Indeed, the above suggested formula is correct: per the last observation in the comment to A156623 analyzing this register machine, a(n) = 3*(A156623(n+1)-1)+1 = 3*A156623(n+1) - 2 = 3*A061419(n+1) - 2 = A070885(n+1) - 2. - Glen Whitney, Aug 04 2018


Cf. A061419, A070885.

Cf. A156623 for analogous sequence for register b.

Sequence in context: A190845 A190805 A008471 * A111314 A316861 A298354

Adjacent sequences: A156619 A156620 A156621 * A156623 A156624 A156625




Jack W Grahl, Feb 11 2009


Rousseau's suggested formula verified by Glen Whitney, Aug 03 2018



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