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A323462
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Smallest number that can be obtained from the "Choix de Bruxelles", version 2 (A323460) operation applied to n.
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0
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1, 1, 3, 2, 5, 3, 7, 4, 9, 5, 11, 6, 13, 7, 15, 8, 17, 9, 19, 10, 11, 11, 13, 12, 15, 13, 17, 14, 19, 15, 31, 16, 33, 17, 35, 18, 37, 19, 39, 20, 21, 21, 23, 22, 25, 23, 27, 24, 29, 25, 51, 26, 53, 27, 55, 28, 57, 29, 59, 30, 31, 31, 33, 32, 35, 33, 37, 34, 39, 35, 71, 36, 73, 37, 75, 38, 77, 39, 79, 40, 41
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OFFSET
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1,3
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COMMENTS
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Smallest element in row n of irregular triangle in A323460.
Theorem: Let the decimal expansion of n be d_1 d_2 ... d_k. (i) If there is a substring d_r ... d_s which starts with d_r = 1 and ends with an even digit d_s = e, take that string which starts with the leftmost 1 and ends with the rightmost even digit, and halve it. (ii) Otherwise, if there is an even digit e, take the substring from d_1 to the rightmost such e and halve it. (iii) Otherwise, all d_i are odd, and a(n) = n.
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LINKS
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Table of n, a(n) for n=1..81.
Eric Angelini, Lars Blomberg, Charlie Neder, Remy Sigrist, and N. J. A. Sloane, "Choix de Bruxelles": A New Operation on Positive Integers, arXiv:1902.01444, Feb 2019; Fib. Quart. 57:3 (2019), 195-200.
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EXAMPLE
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From 23 we can reach any of 13, 43, 26, 46, and the smallest of these is a(23) = 13.
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CROSSREFS
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Cf. A323286, A323460, A323288.
Sequence in context: A076605 A318516 A194748 * A030640 A176447 A145051
Adjacent sequences: A323459 A323460 A323461 * A323463 A323464 A323465
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KEYWORD
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nonn,base
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AUTHOR
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N. J. A. Sloane, Jan 23 2019
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STATUS
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approved
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