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 A171884 Lexicographically earliest injective nonnegative sequence a(n) satisfying |a(n+1) - a(n)| = n for all n. 5
 0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, 42, 63, 41, 64, 40, 65, 39, 66, 38, 67, 37, 68, 36, 69, 35, 70, 34, 71, 33, 72, 32, 73, 31, 74, 30, 75, 29, 76, 28, 77, 27, 78, 26, 79, 133, 188, 132, 189, 131, 190, 130, 191, 129, 192, 128, 193, 127, 194 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The map n -> a(n) is an injective map to the nonnegative integers, i.e., no two terms are identical. Appears not to contain numbers from the following sets (grouped intentionally): {4, 5}, {14, 15, 16, 17, 18, 19}, {44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61}, etc. The numbers of terms in these groups appears to be A008776. - Paul Raff, Mar 15 2010 The first 23 terms are shared with Recamán's sequence A005132, but from then on they are different. - Philippe Deléham, Mar 01 2013, Omar E. Pol, Jul 01 2013 From M. F. Hasler, May 09 2013: It appears that the starting points of the gaps (4, 14, 44, 134, 404, 1214, ...) are given by A181655(2n) = A198643(n-1), and thus the ending points (5, 19, 61, ...) by A181655(2n) + A048473(n-1). The first differences have signs (grouped intentionally): +++, -, +++, -+-+-+-+- (5 times "-"), +++, -+...+- (17 times "-"), +++, ... where the number of minus signs is again given by A048473 = A008776-1. (End) A correspondent, Dennis Reichard, conjectures that (i) a(n) <= 3.5*n for all n and (ii) the sequence covers 2/3 of all natural numbers. - N. J. A. Sloane, Jun 30 2018 LINKS R. Munafo, main-A171884.c(C source code to generate the sequence) FORMULA a(n+1) = a(n) +- n with - iff n is even but not n = 2 + 2*3^k. (Cf. comment from May 09 2013.) - M. F. Hasler, Apr 05 2019 EXAMPLE We begin with 0, 0+1=1, 1+2=3. 3-3=0 cannot be the next term because 0 is already in the sequence so we go to 3+3=6. The next could be 6-4=2 or 6+4=10 but we choose 2 because it is smaller. MATHEMATICA Contribution from Paul Raff, Mar 15 2010: (Start) A171884[{}, _, _] := {}; A171884[L_List, max_Integer, True] := If[Length[L] == max, L, With[{n = Length[L]},   If[Last[L] - n < 1 || MemberQ[L, Last[L] - n],     If[MemberQ[L, Last[L] + n],        A171884[Drop[L, -1], max, False],        A171884[Append[L, Last[L] + n], max, True]],     A171884[Append[L, Last[L] - n], max, True]]]] A171884[L_List, max_Integer, False] := With[{n = Length[L]},   If[MemberQ[L, Last[L] + n],      A171884[Drop[L, -1], max, False],      A171884[Append[L, Last[L] + n], max, True]]] A171884[{0}, 200, True] (End) PROG (PARI) A171884_upto(N, a=0, t=2)=vector(N, k, a+=if(!bitand(k, 1), k-1, t-=1, 1-k, t=k-1)) \\ or: A171884_upto(N, a)=vector(N, k, a+=if(bitand(k, 1)&&k\2!=3^valuation(k-(k>1), 3), 1-k, k-1)) \\ M. F. Hasler, Apr 05 2019 CROSSREFS Cf. A005132, which allows duplicate values. Cf. also A118201, in which every value of a(n) and of |a(n+1)-a(n)| occurs exactly once, but does not ensure that the latter is strictly increasing. Sequence in context: A274647 A113880 A339192 * A339557 A226940 A098141 Adjacent sequences:  A171881 A171882 A171883 * A171885 A171886 A171887 KEYWORD nonn AUTHOR Robert Munafo, Mar 11 2010 EXTENSIONS Definition edited by M. F. Hasler, Apr 01 2019 STATUS approved

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Last modified May 16 10:47 EDT 2021. Contains 343941 sequences. (Running on oeis4.)