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A112258
Numbers n not divisible by 10 such that the decimal representation of n^26 does not use every nonzero digit.
0
1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 17, 23, 29, 39, 61, 81, 95, 119, 164, 242, 5193, 9004, 23432, 246968, 8876708, 32886598, 2141194665
OFFSET
1,2
COMMENTS
Multiples of 10 are excluded because (10*n)^k uses the same nonzero digits as n^k. - Is the sequence finite?
Similar sequences can be defined for other positive integer exponents. 26 is the smallest exponent such that the corresponding sequence has less than 30 terms < 10^8.
a(29) > 10^11, if it exists. - Chai Wah Wu, Sep 19 2018
LINKS
Patrick De Geest, The Nine Digits Page
Eric Weisstein's World of Mathematics, Pandigital
EXAMPLE
5^26 = 1490116119384765625 uses every digit, so 5 is not in the sequence.
6^26 = 170581728179578208256 does not use digits 3 and 4, so 6 is a term.
PROG
(PARI) {e=26; for(n=1, 350000, if(n%10>0, v=vector(9); c=0; k=n^e; while(c<9&&k>0, g=divrem(k, 10); k=g[1]; if(g[2]>0&&v[g[2]]==0, v[g[2]]=1; c++)); if(c<9, print1(n, ", "))))}
(Python)
A112258_list = [n for n in range(1, 10**6) if n % 10 and len(set(str(n**26))) < 10] # Chai Wah Wu, May 31 2015
CROSSREFS
Cf. A089081 (26th powers).
Sequence in context: A225837 A035246 A356955 * A032893 A032852 A031990
KEYWORD
nonn,base,more
AUTHOR
Klaus Brockhaus, Aug 30 2005
EXTENSIONS
a(28) from Lars Blomberg, Sep 25 2011
STATUS
approved