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 A082850 Let S(0) = {}, S(n) = {S(n-1), S(n-1), n}; sequence gives S(infinity). 5
 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 4, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 4, 5, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 4, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 4, 5, 6, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 4, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 4, 5, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Sequence counts up to successive values of A001511; i.e. apply the morphism k -> 1,2,...,k to A001511. If all 1's are removed from the sequence, the resulting sequence b has b(n) = a(n)+1. A101925 is the positions of 1's in this sequence. LINKS FORMULA a(2^m-1)=m a(2^m-1) = m. If n = 2^m-1 + k, with 0 < k < 2^m, then a(n) = a(k). - Franklin T. Adams-Watters, Aug 16 2006 a(n) = log_2(A182105(n)) + 1. - Laurent Orseau, Jun 18 2019 EXAMPLE S(1) = {1}, S(2) = {1,1,2}, S(3) = {1,1,2,1,1,2,3}, etc. MATHEMATICA Fold[Flatten[{#1, #1, #2}] &, {}, Range[5]] (* Birkas Gyorgy, Apr 13 2011 *) Flatten[Table[Length@Last@Split@IntegerDigits[2 n, 2], {n, 20}] /. {n_ ->Range[n]}] (* Birkas Gyorgy, Apr 13 2011 *) CROSSREFS Cf. A082851 (partial sums). Cf. A001511, A101925. Sequence in context: A116361 A106796 A265743 * A290695 A277446 A088198 Adjacent sequences:  A082847 A082848 A082849 * A082851 A082852 A082853 KEYWORD nonn AUTHOR Benoit Cloitre, Apr 14 2003 STATUS approved

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Last modified October 21 13:24 EDT 2019. Contains 328299 sequences. (Running on oeis4.)