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 A085765 Partial sums and bisection of A086450. 3
 1, 2, 4, 5, 9, 11, 16, 17, 26, 30, 41, 43, 59, 64, 81, 82, 108, 117, 147, 151, 192, 203, 246, 248, 307, 323, 387, 392, 473, 490, 572, 573, 681, 707, 824, 833, 980, 1010, 1161, 1165, 1357, 1398, 1601, 1612, 1858, 1901, 2149, 2151, 2458, 2517 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sum of inverses of a(n) is 1.5398789314089581123... Conjecture: log(a(n))/log(n) grows unboundedly. Conjecture: a(n) mod 2 repeats the 7-pattern 0,0,1,1,1,0,1. The conjecture concerning the mod 2 pattern follows directly from the corresponding conjecture proved in A086450. - Lambert Herrgesell (zero815(AT)googlemail.com), May 08 2007 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 FORMULA a(n) = A086450(2n) = A086450(0) + ... + A086450(n). - Charles R Greathouse IV, Sep 26 2013 MAPLE b:= proc(n) local m; b(n):= `if`(n=0, 1,       `if`(irem(n, 2, 'm')=1, b(m), a(m)))     end: a:= proc(n) a(n):= b(n) +`if`(n=0, 0, a(n-1)) end: seq(a(n), n=0..100);  # Alois P. Heinz, Sep 26 2013 MATHEMATICA b[0] = 1; b[n_] := b[n] = If[EvenQ[n], Sum[b[n/2-k], {k, 0, n/2}], b[(n-1)/2]]; A085765 = Table[b[n], {n, 0, 100}] // Accumulate (* Jean-François Alcover, Mar 28 2017 *) PROG (PARI) v=vector(1000); v[1]=1; s=1; for(n=2, 1000, v[n]=if(n%2==0, v[n/2], s=s+v[(n+1)/2]; print1(s", "); s)) (PARI) lista(nn) = {v=vector(nn); v[1]=1; s=1; for(n = 2, nn, v[n]= if(n%2==0, v[n/2], s=s+v[(n+1)/2])); forstep(i = 1, nn, 2, print1(v[i], ", "); ); } \\ Michel Marcus, Sep 26 2013 CROSSREFS Sequence in context: A258652 A065514 A152186 * A211521 A039871 A161375 Adjacent sequences:  A085762 A085763 A085764 * A085766 A085767 A085768 KEYWORD nonn,easy AUTHOR Ralf Stephan, Jul 22 2003 STATUS approved

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Last modified September 21 13:37 EDT 2019. Contains 327253 sequences. (Running on oeis4.)