A323462 - OEIS

A323462

Smallest number that can be obtained from the "Choix de Bruxelles", version 2 (A323460) operation applied to n.

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

1,3

COMMENTS

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.

LINKS

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.

EXAMPLE

From 23 we can reach any of 13, 43, 26, 46, and the smallest of these is a(23) = 13.

CROSSREFS

Cf. A323286, A323460, A323288.

Sequence in context: A318516 A367728 A194748 * A030640 A176447 A145051

Adjacent sequences: A323459 A323460 A323461 * A323463 A323464 A323465

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Jan 23 2019

STATUS

approved