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A156622
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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]}.
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1
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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
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OFFSET
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1,2
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COMMENTS
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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.
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REFERENCES
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Wolfram, S., A New Kind of Science. Champaign, IL: Wolfram Media, pp. 97-102, 2002.
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LINKS
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FORMULA
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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
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CROSSREFS
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Cf. A156623 for analogous sequence for register b.
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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Rousseau's suggested formula verified by Glen Whitney, Aug 03 2018
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STATUS
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approved
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