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 A335972 The Locomotive Pushing the Wagons to the Right sequence (see Comments lines for definition). 4
 2, 13, 14, 15, 16, 17, 18, 91, 201, 202, 31, 203, 24, 25, 26, 27, 28, 92, 41, 204, 35, 36, 37, 38, 93, 42, 51, 205, 46, 47, 48, 94, 52, 61, 206, 57, 58, 95, 62, 71, 207, 68, 96, 72, 81, 208, 97, 82, 131, 301, 302, 132, 133, 141, 303, 142, 134, 53, 143, 144, 63, 145, 64, 73, 146, 74 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(1) is the (pushing) locomotive; a(2), a(3), a(4),... a(n),... are the wagons. To hook a wagon to its successor (on the right) you must be able to insert the rightmost digit of a(n) between the first two digits of a(n+1). In mathematical terms, the value of the rightmost digit of a(n) must be between (not equal to) the first and the second digit of a(n+1). This is the lexicographically earliest sequence of distinct positive terms with this property. a(n) cannot end in 0 or 9. - Michael S. Branicky, Dec 14 2020 LINKS Carole Dubois, Table of n, a(n) for n = 1..5001 EXAMPLE The sequence starts with 2, 13, 14, 15, 16, 17, 18, 91, 201, 202,... a(1) = 2 as there is no earliest possible (pushing to the right) locomotive; a(2) = 13 starts with 1 and 3: now 1 < 2 < 3 [2 being the rightmost digit of a(1)]; a(3) = 14 starts with 1 and 4: now 1 < 3 < 4 [3 being the rightmost digit of a(2)]; a(4) = 15 starts with 1 and 5: now 1 < 4 < 5 [4 being the rightmost digit of a(3)]; (...) a(8) = 91 starts with 9 and 1: now 9 > 8 > 1 [8 being the rightmost digit of a(7)]; a(9) = 201 starts with 2 and 0: now 2 > 1 > 0 [1 being the rightmost digit of a(8)]; a(10) = 202 starts with 2 and 0: now 2 > 1 > 0 [1 being the rightmost digit of a(9)]; etc. PROG (Python) def dead_end(k): return k%10 in {0, 9} def aupto(n, seed=2):   train, used = [seed], {seed}   for n in range(2, n+1):     caboose = train[-1]     hook = caboose % 10     low2, high2 = 10 + (hook + 1), 90 + (hook - 1)     an, pow10b = low2, 1     while an in used or dead_end(an): an += 1     first2 = an//pow10b     a2, b2 = divmod(first2, 10)     while True:       if a2 < hook < b2 or a2 > hook > b2:         train.append(an)         used.add(an)         break       if first2 > high2:         pow10b *= 10         an = low2*pow10b       else:         an += pow10b         an -= an%pow10b       while an in used or dead_end(an): an += 1       first2 = an//pow10b       a2, b2 = divmod(first2, 10)   return train    # use train[n-1] for a(n) print(aupto(66))  # Michael S. Branicky, Dec 14 2020 CROSSREFS Cf. A335971 (locomotive pulling to the left) and A335973 (two locomotives). Sequence in context: A065584 A153651 A229908 * A320339 A075032 A032932 Adjacent sequences:  A335969 A335970 A335971 * A335973 A335974 A335975 KEYWORD base,nonn AUTHOR Eric Angelini and Carole Dubois, Jul 03 2020 STATUS approved

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Last modified November 26 21:07 EST 2021. Contains 349344 sequences. (Running on oeis4.)