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 A302128 a(n) = a(a(n-2)) + a(n-a(n-1)) with a(1) = a(2) = a(3) = 1. 3
 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 13, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 20, 21, 21, 21, 21, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 32, 33 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS A variation of the Hofstadter-Conway \$10,000 sequence (A004001). Similar with Newman generalization on A004001 (see A005350 and Kleitman's solution in Links section of A005350), a_i(n) is unbounded and slow sequence for all i >= 1 where a_i(n) = a_i(a_i(n-2)) + a_i(n-a_i(n-1)) with i + 1 initial conditions a_i(1) = a_i(2) = ... = a_i(i+1) = 1. In particular, a_1(n) = ceil(n/2). LINKS Altug Alkan, Proof of slowness FORMULA a(n+1) - a(n) = 0 or 1 for all n >= 1 and a(n) hits every positive integer. MAPLE a:=proc(n) option remember: if n<4 then 1 else procname(procname(n-2))+procname(n-procname(n-1)) fi; end: seq(a(n), n=1..100); # Muniru A Asiru, Jun 26 2018 PROG (PARI) a=vector(99); for(n=1, 3, a[n] = 1); for(n=4, #a, a[n] = a[a[n-2]] + a[n-a[n-1]]); a (GAP) a:=[1, 1, 1];; for n in [4..100] do a[n]:=a[a[n-2]]+a[n-a[n-1]]; od; a; # Muniru A Asiru, Jun 26 2018 CROSSREFS Cf. A004001, A005229, A005350. Sequence in context: A288156 A248515 A194986 * A054071 A028827 A083055 Adjacent sequences:  A302125 A302126 A302127 * A302129 A302130 A302131 KEYWORD nonn,easy AUTHOR Altug Alkan, Jun 20 2018 STATUS approved

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Last modified September 19 11:06 EDT 2019. Contains 327192 sequences. (Running on oeis4.)