A034704 Largest number that can be made using only the digits of n, exponentiation and concatenation.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 21, 31, 41, 51, 61, 71, 81, 91, 20, 21, 22, 32, 42, 52, 64, 128, 256, 512, 30, 31, 32, 33, 81, 243, 729, 2187, 6561, 19683, 40, 41, 42, 81, 256, 1024, 4096, 16384, 65536, 262144, 50, 51, 52, 243, 1024, 3125, 15625, 78125

Offset

1,2

Links

Dominic McCarty, Table of n, a(n) for n = 1..237

Dominic McCarty, Log-log scatterplot of first 1000 terms

Example

Using exponentiation and concatenation, the digits of 25 can be arranged to yield: 25, 52, 2^5, 5^2. The largest of these is 52, so a(25) = 52.
Using exponentiation and concatenation, the digits of 26 can be arranged to yield: 26, 62, 2^6, 6^2. The largest of these is 2^6, so a(26) = 2^6 = 64.

Prog

(Python)
def a(n):
    if n < 10: return n
    d = sorted(map(int, list(str(n))))
    for q in [1, 0]:
        while q in d and (i := d.index(q)) != len(d)-1:
            d.pop(i)
            d[-1] = (d[-1]*10)+q
    for q, r in [(2, 5), (3, 3)]:
        if (len(d)) == 1: return d[0]
        if d[-2] == q and d[-1] <= r:
            d.pop(-2)
            d[-1] = (d[-1]*10)+q
    for i in range(len(d)-2, -1, -1): d[i] = d[i] ** d[i+1]
    return d[0] # Dominic McCarty, Mar 15 2025

Crossrefs

Sequence in context: A225805 A068637 A004186 * A362076 A276512 A023792

Adjacent sequences: A034701 A034702 A034703 * A034705 A034706 A034707

Keyword

nonn,base,nice

Author

Erich Friedman

Status

approved