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A029790
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None of the digits in k is present in k^2 or k^3.
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3
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2, 3, 7, 8, 22, 47, 53, 77, 92, 157, 187, 188, 192, 552, 558, 577, 707, 772, 922, 2522, 8338, 17177, 66888, 575757, 929522, 1717177, 8888588
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OFFSET
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1,1
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COMMENTS
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If it exists, a(28) > 10^9. - Derek Orr, Jul 13 2014
I strongly conjecture that a(28) does not exist.
If a(28) exists, then a(28) > 10^20.
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LINKS
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EXAMPLE
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For k = 47, k^2 = 2209 and k^3 = 103823. 4 and 7 do not appear in either of these numbers.
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MAPLE
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filter:= proc(n) local S1, S23;
S1:= convert(convert(n, base, 10), set);
S23:= convert(convert(n^2, base, 10), set) union
convert(convert(n^3, base, 10), set);
nops(S1 intersect S23)=0
end proc:
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MATHEMATICA
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Select[Range@ 1000000, Intersection[IntegerDigits[#^2], IntegerDigits@ #] == {} && Intersection[IntegerDigits[#^3], IntegerDigits@ #] == {} &] (* Michael De Vlieger, Jul 23 2015 *)
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PROG
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(Python)
def a(n):
s = str(n)
s2 = str(n**2)
s3 = str(n**3)
count = 0
for i in s:
if s2.count(i) == 0 and s3.count(i) == 0:
count += 1
else:
break
if count == len(s):
return True
n = 1
while n < 10**9:
if a(n):
print(n, end=', ')
n += 1
(PARI) isok(n) = d = vecsort(Set(digits(n))); dd = vecsort(Set(digits(n^2))); ddd = vecsort(Set(digits(n^3))); for (i=1, #d, if (vecsearch(dd, d[i]) || vecsearch(ddd, d[i]), return (0)); ); 1 \\ Michel Marcus, Jul 13 2014
(PARI) is(n)=#setintersect(setunion(Set(digits(n^2)), Set(digits(n^3))), Set(digits(n)))==0 \\ Charles R Greathouse IV, Jul 23 2015
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CROSSREFS
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KEYWORD
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nonn,base,more,hard
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AUTHOR
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STATUS
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approved
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