A112993 Exclusionary cubes: cubes of the terms in A112994.

8, 27, 343, 512, 19683, 79507, 103823, 110592, 140608, 148877, 250047, 314432, 778688, 3869893, 5088448, 6539203, 7077888, 18191447, 54010152, 67917312, 75686967, 96071912, 102503232, 109215352, 115501303, 146363183, 202262003, 224755712

Offset

1,1

Comments

b-file is complete: there are 42 terms. - Michael S. Branicky, Aug 27 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.

Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 60.

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..42 [From the Clifford Pickover link. Conjectured to be the full list of terms.]

Clifford A. Pickover, Extreme Challenges in Mathematics and Morals

Prog

(Python)
def ok(n):
    s = str(n)
    return len(s) == len(set(s)) and set(s) & set(str(n**3)) == set()
print([k**3 for k in range(7659) if ok(k)]) # Michael S. Branicky, Aug 27 2021
(Python) # version for verifying full sequence
from itertools import 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 afull():
    alst = []
    for k in no_repeated_digits():
        if set(str(k)) & set(str(k**3)) == set():
            alst.append(k**3)
    return alst
print(afull()) # Michael S. Branicky, Aug 27 2021

Crossrefs

Cf. A112994.

Sequence in context: A197620 A029786 A029792 * A115694 A028935 A030089

Adjacent sequences: A112990 A112991 A112992 * A112994 A112995 A112996

Keyword

nonn,base,fini,full

Author

Lekraj Beedassy, Oct 13 2005

Extensions

Corrected by N. J. A. Sloane, May 22 2008

Status

approved