This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A129150 #45 Nov 29 2019 20:50:09
%S A129150 8,12,16,32,80,176,368,752,1520,3424,8592,20096,70464,235072,705280,
%T A129150 3023616,13223680,55540736,278539264,1392697344,9541095424,
%U A129150 58609614848,410267320320,3397142953984,24143851798528,176071227916288,1232666139967488,9523075842834432
%N A129150 The n-th arithmetic derivative of 2^3.
%C A129150 Conjecture: a strictly increasing sequence. - _J. Lowell_, Sep 10 2008
%C A129150 The sequence is strictly increasing because (4*n)' = 4*n + 4*n'. - _David Radcliffe_, Aug 19 2014
%C A129150 8 is the smallest integer that has a nontrivial trajectory (not going to 0 nor reduced to a fixed point as 4) under A003415, but 15 = A090636(1) has 8 as second term in its trajectory. 20 is the next larger such integer with a distinct trajectory, but has two larger predecessors, cf. A090635. - _M. F. Hasler_, Nov 27 2019
%C A129150 In general, the trajectory of p^(p+1) under A003415 has a common factor p^p, and divided by p^p it gives the trajectory of p under A129283: n -> n + n'. Here we have the case p = 2 (see A129284 for a(n)/2^2), cf. A129151 and A129152 for p = 3 and 5. - _M. F. Hasler_, Nov 28 2019
%H A129150 Charles R Greathouse IV, <a href="/A129150/b129150.txt">Table of n, a(n) for n = 0..100</a>
%F A129150 a(n+1) = A003415(a(n)), a(0) = 2^3 = 8.
%F A129150 a(n) = A090636(n+2).
%F A129150 A129251(a(n)) > 0. - _Reinhard Zumkeller_, Apr 07 2007
%F A129150 a(n) = 4*A129284(n). - _M. F. Hasler_, Nov 27 2019
%t A129150 dn[0] = 0; dn[1] = 0; dn[n_?Negative] := -dn[-n]; dn[n_] := Module[{f = Transpose[FactorInteger[n]]}, If[PrimeQ[n], 1, Total[n*f[[2]]/f[[1]]]]]; s = 2^3; Join[{s}, Table[s = dn[s], {28}]] (* _T. D. Noe_, Mar 07 2013 *)
%o A129150 (Haskell)
%o A129150 a129150 n = a129150_list !! n
%o A129150 a129150_list = iterate a003415 8 -- _Reinhard Zumkeller_, Apr 29 2012
%o A129150 (PARI) A129150(n,a=8)={if(n<0, vector(-n,n, if(n>1, a=A003415(a), a)), for(n=1,n, a=A003415(a)); a)} \\ For n<0 return the vector a[0..-n-1]. - _M. F. Hasler_, Nov 27 2019
%Y A129150 Cf. A129151, A129152, A068327, A099309, A051674, A100716, A129284.
%Y A129150 Row n = 8 of A258651.
%K A129150 nonn
%O A129150 0,1
%A A129150 _Reinhard Zumkeller_, Apr 01 2007
%E A129150 a(21)-a(27) from _Paolo P. Lava_, Apr 16 2012