A112994 Numbers whose cubes are exclusionary: numbers k such that k has no repeated digits and k and k^3 have no digits in common.

2, 3, 7, 8, 27, 43, 47, 48, 52, 53, 63, 68, 92, 157, 172, 187, 192, 263, 378, 408, 423, 458, 468, 478, 487, 527, 587, 608, 648, 692, 823, 843, 918, 1457, 1587, 1592, 4657, 4732, 5692, 6058, 6378, 7658

Offset

1,1

Comments

A number k with no repeated digits has an exclusionary cube k^3 if the latter is made up of digits not appearing in k. (This is a subsequence of A029785.) For the corresponding exclusionary cubes see A112993. Conjectured to be complete.

Data are 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

Table of n, a(n) for n=1..42.

Clifford A. Pickover, Extreme Challenges in Mathematics and Morals

Mathematica

Select[Range[8000], Max[DigitCount[#]]==1&&Intersection[IntegerDigits[ #], IntegerDigits[#^3]]=={}&] (* Harvey P. Dale, Sep 06 2021 *)

Prog

(PARI) isok(n) = my(digs = digits(n)); (#digs == #Set(digs)) && (#setintersect(Set(digs), Set(digits(n^3))) == 0); \\ Michel Marcus, Oct 26 2013
(Python)
def ok(n):
    s = str(n)
    return len(s) == len(set(s)) and set(s) & set(str(n**3)) == set()
print([k 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)
    return alst
print(afull()) # Michael S. Branicky, Aug 27 2021

Crossrefs

Subsequence of A029785.

The corresponding cubes are in A112993.

Sequence in context: A206725 A129645 A324481 * A056036 A056432 A271506

Adjacent sequences: A112991 A112992 A112993 * A112995 A112996 A112997

Keyword

nonn,base,fini,full

Author

Lekraj Beedassy, Oct 13 2005

Extensions

Missing term 468 added by N. J. A. Sloane, May 22 2008

Definition clarified by Harvey P. Dale, Sep 06 2021

Status

approved