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 A188163 Smallest m such that A004001(m) = n. 14
 1, 3, 5, 6, 9, 10, 11, 13, 17, 18, 19, 20, 22, 23, 25, 28, 33, 34, 35, 36, 37, 39, 40, 41, 43, 44, 46, 49, 50, 52, 55, 59, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 77, 78, 79, 81, 82, 84, 87, 88, 89, 91, 92, 94, 97, 98, 100, 103, 107, 108, 110, 113, 117, 122 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS How is this related to A088359? - R. J. Mathar, Jan 09 2013 It is not hard to show that a(n) exists for all n, and in particular a(n) < 2^n. - Charles R Greathouse IV, Jan 13 2013 From Antti Karttunen, Jan 10 & 18 2016: (Start) Positions of records in A004001. After 1 the positions where A004001 increases (by necessity by one). An answer to the question of R. J. Mathar above: This sequence is equal to A088359 with prepended 1. This follows because at each of its unique values (terms of A088359), A004001 must grow, but it can grow nowhere else. See Kubo and Vakil paper and especially the illustrations of Q and R-trees on pages 229-230 (pages 5 & 6 in PDF) and also in sequence A265332. Obviously A004001 can obtain unique values only at points which form a subset (A266399) of this sequence. (End) LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 T. Kubo and R. Vakil, On Conway's recursive sequence, Discr. Math. 152 (1996), 225-252. User "Panurge", Frankl's conjecture and Oeis sequence A188163, Mathoverflow.net, Mar 29 2016. Wikipedia, Hofstadter sequence Eric Weisstein's World of Mathematics, Hofstadter-Conway \$10,000 Sequence. FORMULA Other identities. For all n >= 1: A004001(a(n)) = n and A004001(m) < n for m < a(n). A051135(n) = a(n+1) - a(n). MAPLE A188163 := proc(n)     for a from 1 do         if A004001(a) = n then             return a;         end if;     end do: end proc: # R. J. Mathar, May 15 2013 MATHEMATICA h = 1; h = 1; h[n_] := h[n] = h[h[n-1]] + h[n - h[n-1]]; a[n_] := For[m = 1, True, m++, If[h[m] == n, Return[m]]]; Array[a, 64] (* Jean-François Alcover, Jan 27 2018 *) PROG (Haskell) import Data.List (elemIndex) import Data.Maybe (fromJust) a188163 n = succ \$ fromJust \$ elemIndex n a004001_list (Scheme) (define A188163 (RECORD-POS 1 1 A004001)) ;; Code for A004001 given in that entry. Uses also my IntSeq-library. - Antti Karttunen, Jan 18 2016 CROSSREFS Equal to A088359 with prepended 1. Column 1 of A265901, Row 1 of A265903. Cf. A051135 (first differences). Cf. A087686 (complement, apart from the initial 1). Cf. A004001 (also the least monotonic left inverse of this sequence). Cf. A093879, A265332. Cf. A266399 (a subsequence). Sequence in context: A056875 A308011 A087757 * A088359 A184413 A187345 Adjacent sequences:  A188160 A188161 A188162 * A188164 A188165 A188166 KEYWORD nonn AUTHOR Reinhard Zumkeller, Jun 03 2011 STATUS approved

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Last modified August 24 22:49 EDT 2019. Contains 326314 sequences. (Running on oeis4.)