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 A246093 Paradigm shift sequence for (3,3) production scheme with replacement. 9
 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 21, 24, 27, 30, 33, 36, 40, 44, 48, 52, 56, 60, 65, 72, 81, 90, 99, 108, 120, 132, 144, 160, 176, 192, 208, 224, 243, 270, 297, 324, 360, 396, 432, 480, 528, 576, 640, 704, 768, 832, 896, 972, 1080, 1188, 1296, 1440, 1584, 1728, 1920, 2112, 2304, 2560, 2816, 3072, 3328, 3584, 3888, 4320, 4752, 5184 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This sequence is the solution to the following problem: "Suppose you have the choice of using one of three production options: apply a simple incremental action, bundle existing output as an integrated product (which requires p=3 steps), or implement the current bundled action (which requires q=3 steps). The first use of a novel bundle erases (or makes obsolete) all prior actions.  How large an output can be generated in n time steps?" 1. A production scheme with replacement R(p,q) eliminates existing output following a bundling action, while an additive scheme A(p,q) retains the output. The schemes correspond according to A(p,q)=R(p-q,q), with the replacement scheme serving as the default presentation. 2. This problem is structurally similar to the Copy and Paste Keyboard problem: Existing sequences (A178715 and A193286) should be regarded as Paradigm-Shift Sequences with production schemes R(1,1) and R(2,1) with replacement, respectively. 3. The ideal number of implementations per bundle, as measured by the geometric growth rate (p+zq root of z), is z = 4. 4. All solutions will be of the form a(n) = (qm+r) * m^b * (m+1)^d. LINKS FORMULA a(n) = (qd+r) * d^(C-R) * (d+1)^R, where r = (n-Cp) mod q, Q = floor( (R-Cp)/q ), R = Q mod (C+1), and d = floor ( Q/(C+1) ). Recursive:  a(n) = 4*a(n-15) for all n >= 48. CROSSREFS Paradigm shift sequences with q=3: A029747, A029750, A246077, A246081, A246085, A246089, A246093, A246097, A246101. Paradigm shift sequences with p=3: A193455, A246092, A246093, A246094, A246095. Sequence in context: A246079 A246086 A194417 * A261924 A255421 A255407 Adjacent sequences:  A246090 A246091 A246092 * A246094 A246095 A246096 KEYWORD nonn AUTHOR Jonathan T. Rowell, Aug 13 2014 STATUS approved

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Last modified May 12 07:28 EDT 2021. Contains 343821 sequences. (Running on oeis4.)