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 A308092 The sum of the first n terms of the sequence is the concatenation of the first n bits of the sequence read as binary, with a(1) = 1. 2
 1, 2, 3, 7, 14, 28, 56, 112, 224, 448, 896, 1791, 3583, 7166, 14332, 28663, 57326, 114653, 229306, 458612, 917223, 1834446, 3668892, 7337785, 14675570, 29351140, 58702279, 117404558, 234809116, 469618232, 939236465, 1878472930, 3756945860, 7513891719 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS In binary, the sequence begins 1, 10, 11, 111, 1110, 11100, 111000, 1110000, 11100000, 111000000, 1110000000, 11011111111, 110111111111, 1101111111110, 11011111111100, ... Conjecture: The number of 1's in the binary representation of each term is weakly increasing, i.e., A000120(a(n)) >= A000120(a(n-1)). Proved by Matthew Scroggs; see link. - Peter Kagey, Jun 19 2019 LINKS Peter Kagey, Table of n, a(n) for n = 1..1000 Matthew Scroggs, Number of 1s in A308092 FORMULA a(n) = c(n) - c(n-1) for n > 2, where c(n) is the concatenation of the first n bits of the sequence. EXAMPLE For n=5, 1 + 2 + 3 + 7 + 14 = 1_2 + 10_2 + 11_2 + 111_2 + 1110_2 = 11011_2, the first five bits of the sequence. PROG (Ruby) def first_bits(n, seq); seq.map { |i| i.to_s(2) }.join[0...n].to_i(2) end def next_term(n, seq); first_bits(n, seq) - first_bits(n-1, seq) end def a308092_list(n)   (3..n).reduce([1, 2]) { |accum, i| accum << next_term(i, accum) } end CROSSREFS Cf. A000120, A300000 (decimal analog). Sequence in context: A078043 A294627 A293326 * A262765 A131666 A135258 Adjacent sequences:  A308089 A308090 A308091 * A308093 A308094 A308095 KEYWORD nonn,base AUTHOR Peter Kagey, May 12 2019 STATUS approved

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Last modified August 19 21:19 EDT 2019. Contains 326133 sequences. (Running on oeis4.)