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A323288 Largest number that can be obtained from the "Choix de Bruxelles", version 2 (A323460) operation applied to n. 4
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 110, 112, 114, 116, 118, 40, 42, 44, 46, 48, 210, 212, 214, 216, 218, 60, 62, 64, 66, 68, 310, 312, 314, 316, 318, 80, 82, 84, 86, 88, 410, 412, 414, 416, 418, 100, 102, 104, 106, 108, 510, 512, 514, 516, 518 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Equally, this is the largest number that can be obtained from the "Choix de Bruxelles", version 1 (A323286) operation applied to n.
Maximal element in row n of irregular triangle in A323460 (or, equally, A323286).
Conjecture: If n contains no digit >= 5, then a(n) = 2*n; otherwise, a(n) is obtained from n by doubling the substring from the last digit >= 5 to the last digit. - Charlie Neder, Jan 19 2019. (This is true. - N. J. A. Sloane, Jan 22 2019)
Corollary: a(n)/n < 10 for all n, and a(n) = 10 - 1/k + O(1/k^2) for n = 10*k+5. - N. J. A. Sloane, Jan 23 2019
The high-water marks for a(n)/n occur at n = 1,15,25,35,45,..., cf. A017329. - N. J. A. Sloane, Jan 23 2019
LINKS
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 [math.NT], Feb 2019; Fib. Quart. 57:3 (2019), 195-200.
FORMULA
a(n) >= 2*n. - Rémy Sigrist, Jan 15 2019
PROG
(PARI) a(n, base=10) = { my (d=digits(n, base), v=2*n); 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]); v = max(v, fromdigits(concat([h, digits(m*2, base), t]), base))))); v } \\ Rémy Sigrist, Jan 15 2019
(Python)
def a(n):
s, out = str(n), {n}
for l in range(1, len(s)+1):
for i in range(len(s)+1-l):
if s[i] == '0': continue
t = int(s[i:i+l])
out.add(int(s[:i] + str(2*t) + s[i+l:]))
if t&1 == 0: out.add(int(s[:i] + str(t//2) + s[i+l:]))
return max(out)
print([a(n) for n in range(1, 60)]) # Michael S. Branicky, Jul 24 2022
CROSSREFS
Sequence in context: A194396 A321193 A284788 * A322131 A209211 A064676
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Jan 15 2019
EXTENSIONS
More terms from Rémy Sigrist, Jan 15 2019
STATUS
approved

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)