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A342072
Lexicographically earliest sequence of distinct positive numbers such that for any n > 0, a(n+1) can be obtained by replacing in the decimal representation of a(n) some nonempty substring m (without leading zero) by a divisor of m or by a positive multiple of m.
2
1, 2, 4, 8, 16, 11, 12, 3, 6, 18, 9, 27, 17, 34, 14, 7, 21, 22, 24, 28, 48, 41, 42, 44, 84, 81, 82, 86, 26, 13, 19, 29, 23, 43, 46, 92, 32, 31, 33, 36, 66, 61, 62, 64, 68, 38, 76, 71, 72, 74, 37, 67, 127, 47, 87, 167, 117, 39, 69, 63, 123, 113, 111, 112, 56
OFFSET
1,2
COMMENTS
The procedure used to generate the terms of this sequence has similarities with that described in A323286 (Choix de Bruxelles); however here, we don't limit ourselves to divide or multiply by two.
Apparently, all positive integers appear in this sequence.
Multiples of 5 are clustered.
LINKS
Rémy Sigrist, Colored scatterplot of the first 10000 terms (red pixels correspond to five clusters of multiples of 5)
EXAMPLE
The first terms, alongside the substitution that gives a(n+1), are:
n a(n) a(n+1)
-- ---- ------
1 1 (1*2)
2 2 (2*2)
3 4 (4*2)
4 8 (8*2)
5 16 1(6/6)
6 11 1(1*2)
7 12 (12/4)
8 3 (3*2)
9 6 (6*3)
10 18 (18/2)
11 9 (9*3)
12 27 (2/2)7
13 17 (17*2)
14 34 (3/3)4
15 14 (14/2)
PROG
(PARI) See Links section.
CROSSREFS
Cf. A323286.
Sequence in context: A167421 A020954 A070347 * A095915 A208278 A036120
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Feb 27 2021
STATUS
approved