A323287 - OEIS

%I #33 Jan 09 2025 13:01:42

%S 1,2,1,2,1,2,1,2,1,2,3,5,3,5,3,5,3,5,3,2,4,6,4,6,4,6,4,6,4,2,3,5,3,5,

%T 3,5,3,5,3,2,4,6,4,6,4,6,4,6,4,2,3,5,3,5,3,5,3,5,3,2,4,6,4,6,4,6,4,6,

%U 4,2,3,5,3,5,3,5,3,5,3,2,4,6,4,6,4,6,4

%N Number of different numbers that can be obtained from (the decimal expansion of) n by one step of the Choix de Bruxelles, version 1 (A323286) operation.

%C This is the number of terms in row n of the irregular triangle in A323286.

%C This is one less than the number of different numbers that can be obtained from (the decimal expansion of) n by one step of the Choix de Bruxelles, version 2 (A323460) operation. In other words, this is one less than the number of terms in row n of the irregular triangle in A323460.

%H Rémy Sigrist, <a href="/A323287/b323287.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Angelini, Lars Blomberg, Charlie Neder, Remy Sigrist, and N. J. A. Sloane, <a href="http://arxiv.org/abs/1902.01444">"Choix de Bruxelles": A New Operation on Positive Integers</a>, arXiv:1902.01444 [math.NT], Feb 2019; Fib. Quart. 57:3 (2019), 195-200.

%H Eric Angelini, Lars Blomberg, Charlie Neder, Remy Sigrist, and N. J. A. Sloane,, <a href="/A307635/a307635.pdf">"Choix de Bruxelles": A New Operation on Positive Integers</a>, Local copy.

%e From 12 we can reach any of 6, 11, 14, 22, 24, so a(12) = 5.

%o (PARI) a(n, base=10) = { my (d=digits(n, base), s=Set()); for (w=1, #d, for (l=0, #d-w, if (d[l+1], my (h=d[1..l], m=fromdigits(d[l+1..l+w], base), t=d[l+w+1..#d]); s = setunion(s, Set(fromdigits(concat([h,digits(m*2,base),t]), base))); if (m%2==0, s = setunion(s, Set(fromdigits(concat([h,digits(m/2,base),t]), base))))))); #s } \\ _Rémy Sigrist_, Jan 15 2019

%o (Python)

%o def a(n):

%o     s, out = str(n), set()

%o     for l in range(1, len(s)+1):

%o         for i in range(len(s)+1-l):

%o             if s[i] == '0': continue

%o             t = int(s[i:i+l])

%o             out.add(int(s[:i] + str(2*t) + s[i+l:]))

%o             if t&1 == 0: out.add(int(s[:i] + str(t//2) + s[i+l:]))

%o     return len(out)

%o print([a(n) for n in range(1, 88)]) # _Michael S. Branicky_, Jul 24 2022

%Y Cf. A323286, A323460.

%K nonn,base

%O 1,2

%A _N. J. A. Sloane_, Jan 14 2019

%E More terms from _Rémy Sigrist_, Jan 15 2019