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 A330896 Lexicographically earliest sequence of positive integers such that for any m > 0, gaps between consecutive m's are all distinct. 2
 1, 1, 2, 1, 2, 2, 1, 3, 2, 3, 1, 4, 2, 3, 3, 1, 4, 2, 4, 3, 5, 1, 3, 2, 4, 4, 5, 5, 1, 3, 2, 5, 4, 5, 6, 3, 1, 6, 2, 6, 4, 5, 7, 3, 4, 1, 5, 2, 6, 5, 7, 7, 3, 4, 6, 1, 4, 2, 5, 6, 6, 7, 3, 7, 6, 5, 1, 4, 2, 7, 8, 6, 7, 3, 8, 5, 7, 4, 1, 6, 2, 7, 8, 8, 9, 3, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Every positive integer appears infinitely many times in the sequence. This sequence has similarities with A003602, where gaps between consecutive equal values are all distinct. This sequence has similarities with A002260, where for any m > 0, gaps between consecutive m's are strictly increasing. Apparently, for any m > 0: - the k-th gap between consecutive m's equals k except for finitely many k's, - the k-th occurrence of m appears at index A330897(m) + A000217(k-1) except for finitely many k's. LINKS Rémy Sigrist, Table of n, a(n) for n = 1..10000 Rémy Sigrist, PARI program for A330896 FORMULA a(n) = 1 iff n belongs to A000124. EXAMPLE The first terms, alongside the gaps for m = 1..4, are:      n|  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23  ...   a(n)|  1  1  2  1  2  2  1  3  2  3  1  4  2  3  3  1  4  2  4  3  5  1  3  ...   ----+---------------------------------------------------------------------    1's|     1,    2,       3,          4,             5,                6,    ...    2's|              2, 1,       3,          4,             5,                ...    3's|                             2,          4, 1,             5,       3, ...    4's|                                                  5,    2,             ... PROG (PARI) See Links section. CROSSREFS Cf. A000124, A000217, A002260, A003602, A330897. Sequence in context: A194083 A109699 A301563 * A328294 A029283 A264404 Adjacent sequences:  A330893 A330894 A330895 * A330897 A330898 A330899 KEYWORD nonn,look AUTHOR Rémy Sigrist, May 01 2020 STATUS approved

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Last modified January 16 15:53 EST 2021. Contains 340206 sequences. (Running on oeis4.)