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 A274069 a(n) is the concatenation of a(n-1) and the Hamming distance between a(n-1) and its reverse (i.e., the minimum number of bitflips needed to make them identical). Sequence written in binary. 1
 1, 10, 1010, 1010100, 101010010, 101010010110, 101010010110100, 101010010110100100, 1010100101101001001000, 10101001011010010010001110, 101010010110100100100011101100, 10101001011010010010001110110010100, 101010010110100100100011101100101001100, 10101001011010010010001110110010100110011000, 10101001011010010010001110110010100110011000100000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..15. EXAMPLE Let a'(n) be the reverse of a(n). E.g., if a(n) = 10100, then a'(n) = 00101. Let hamm(b,c) denote the Hamming distance between b and c. Let concat designate concatenation of arguments. a(1):=1. a(2) is the concatenation of a(1) and hamm(a(1),a'(1)). a'(1) = 1. So hamm(a(1),a'(1)) = hamm('1','1') = 0. So a(2) = concat('1','0') = 10. a(3) is the concatenation of a(2) and hamm(a(2),a'(2)). hamm(a(2),a'(2)) = hamm('10','01') = 2 or 10 in base 2. So a(3) = concat('10','10') = 1010. a(4) is the concatenation of a(3) and hamm(a(3),a'(3)). hamm(a(3),a'(3)) = hamm('1010','0101') = 4 or 100 in base 2. So a(3) = concat('1010','100') = 10100. MAPLE A274069aux := proc(n) option remember; if n = 1 then [1]; else d := procname(n-1) ; dreve := ListTools[Reverse](d) ; ham := 0 ; for i from 1 to nops(d) do if op(i, d) <> op(i, dreve) then ham := ham+1 ; end if; end do: if ham = 0 then [op(d), 0] ; else ListTools[Reverse](convert(ham, base, 2)) ; [op(d), op(%) ] ; end if ; end if; end proc: A274069 := proc(n) digcatL(A274069aux(n)) ; end proc: seq(A274069(n), n=1..30) ; # R. J. Mathar, May 08 2019 CROSSREFS Cf. A144078. Sequence in context: A303610 A080120 A300571 * A325493 A006937 A037220 Adjacent sequences: A274066 A274067 A274068 * A274070 A274071 A274072 KEYWORD nonn,base,easy AUTHOR Meir-Simchah Panzer, Jun 09 2016 EXTENSIONS Edited by Meir-Simchah Panzer, Jun 12 2018 More terms from R. J. Mathar, May 08 2019. STATUS approved

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Last modified August 14 15:29 EDT 2024. Contains 375165 sequences. (Running on oeis4.)