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 A327977 Breadth-first reading of the subtree rooted at 7 of the tree where each parent node is the arithmetic derivative (A003415) of all its children. 7
 7, 10, 21, 25, 18, 38, 46, 65, 77, 217, 361, 129, 205, 493, 529, 98, 426, 718, 170, 254, 462, 982, 1501, 2077, 2257, 2105, 2933, 6953, 11513, 14393, 16469, 17813, 19769, 21653, 24053, 25769, 27413, 29993, 34553, 35369, 41273, 42233, 42869, 44969, 45113, 45173, 11917, 27757, 38881, 45937, 62317, 76897, 84781, 102637, 111457, 114481, 117217, 118477, 120781, 127117, 128881, 501, 1141 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Permutation of A328117. The branching degree of vertex v is given by A099302(v). Leaves form a subsequence of A098700. For any number k at level n (where 7 is at level 2), we have A256750(k) = A327966(k) = n. Question: Does this subtree contain infinitely long paths? How many? Cf. conjecture number 8 in Ufnarovski and Ahlander paper. As an example of possible beginning of such a sequence they give: 1 ← 7 ← 10 ← 25 ← 46 ← 129 ← 170 ← 501 ← 414 ← 2045. LINKS Antti Karttunen, Table of n, a(n) for n = 1..204 Victor Ufnarovski and Bo Ahlander, How to Differentiate a Number, J. Integer Seqs., Vol. 6, 2003. EXAMPLE The subtree is laid out as below. The terms of this sequence are obtained by scanning each successive level of the tree from left to right, from the node 7 onward: (0) | (1) | 7 | 10______________________________ | | 21________ 25 | | | 18___ 38_____ 46_________________________________ | | | | | | | | 65 77 217 361____ 129____ 205 493_____ 529 | | | | | | | 98 426 718 170 254 462 982 | | | | | | |        On the last level illustrated above, the numbers in brackets [ ] tell how many children the node has. E.g, there are three for 98: 1501, 2077, 2257, as A003415(1501) = A003415(2077) = A003415(2257) = 98, and nine for 170: 501, 1141, 2041, 2869, 4309, 5461, 6649, 6901, 7081. PROG (PARI) A002620(n) = ((n^2)>>2); A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac), n*fac[i, 2]/fac[i, 1]))}; \\ From A003415 A327977list(e) = { my(lista=List(), f); for(i=1, e, f = lista[i]; for(k=1, 1+A002620(f), if(A003415(k)==f, listput(lista, k)))); Vec(lista); }; (PARI) \\ With precomputed large A328117, use this: v328117 = readvec("a328117.txt"); A327977list(e) = { my(lista=List(), f, i); for(n=1, e, f = lista[n]; print("n=", n, " #lista=", #lista, " A002620(", f, ")=", A002620(f)); my(u=1+A002620(f)); if(u>=v328117[#v328117], print("Not enough precomputed terms of A328117 as search upper limit ", u, " > ", v328117[#v328117], " (the last item in v328117). Number of expansions so far=", n); return(1/0)); i=1; while(v328117[i] 1: n = n-1 else: return(z) take(52, A327977()) CROSSREFS Cf. A003415, A098699, A098700, A099302, A099303, A099307, A099308, A189760, A256750, A327966, A327968, A328117. Cf. A327975 for the subtree starting from 5, and also A263267 for another similar tree. Sequence in context: A249942 A300021 A363292 * A097634 A120312 A074377 Adjacent sequences: A327974 A327975 A327976 * A327978 A327979 A327980 KEYWORD nonn,tabf AUTHOR Antti Karttunen, Oct 02 2019 STATUS approved

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Last modified October 2 23:30 EDT 2023. Contains 365841 sequences. (Running on oeis4.)