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A113951 Largest number whose n-th power is exclusionary (or 0 if no such number exists). 4
639172, 7658, 2673, 0, 92, 93, 712, 0, 18, 12, 4, 0, 37, 0, 9, 0, 0, 3, 4, 0, 7, 2, 7, 0, 8, 3, 9, 0, 0, 0, 0, 0, 3, 2, 2, 0, 0, 7, 3, 0, 2, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

The number m with no repeated digits has an exclusionary n-th power m^n if the latter is made up of digits not appearing in m. For the corresponding m^n see A113952. In principle, no exclusionary n-th power exists for n == 1 (mod 4) = A016813.

After a(84) = 3, the next nonzero term is a(168) = 2, where 168 is the last known term in A034293. - Michael S. Branicky, Aug 28 2021

REFERENCES

H. Ibstedt, Solution to Problem 2623, "Exclusionary Powers", pp. 346-9 Journal of Recreational Mathematics, Vol. 32 No.4 2003-4, Baywood NY.

LINKS

Michael S. Branicky, Table of n, a(n) for n = 2..225

EXAMPLE

a(4) = 2673 because no number with distinct digits beyond 2673 has a 4th power that shares no digit in common with it (see A111116). Here we have 2673^4 = 51050010415041.

PROG

(Python)

from itertools import combinations, permutations

def no_repeated_digits():

    for d in range(1, 11):

        for p in permutations("0123456789", d):

            if p[0] == '0': continue

            yield int("".join(p))

def a(n):

    m = 0

    for k in no_repeated_digits():

        if set(str(k)) & set(str(k**n)) == set():

            m = max(m, k)

    return m

for n in range(2, 4): print(a(n), end=", ") # Michael S. Branicky, Aug 28 2021

CROSSREFS

Cf. A109135, A112736, A112994, A113318, A034293.

Sequence in context: A250674 A210142 A183745 * A257194 A257187 A254987

Adjacent sequences:  A113948 A113949 A113950 * A113952 A113953 A113954

KEYWORD

nonn,base

AUTHOR

Lekraj Beedassy, Nov 09 2005

EXTENSIONS

a(34), a(39), a(40) corrected by and a(43) and beyond from Michael S. Branicky, Aug 28 2021

STATUS

approved

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Last modified September 24 22:46 EDT 2021. Contains 347651 sequences. (Running on oeis4.)