A112258 Numbers n not divisible by 10 such that the decimal representation of n^26 does not use every nonzero digit.

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

Table of n, a(n) for n=1..28.

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

Adjacent sequences: A112255 A112256 A112257 * A112259 A112260 A112261

Keyword

nonn,base,more

Author

Klaus Brockhaus, Aug 30 2005

Extensions

a(28) from Lars Blomberg, Sep 25 2011

Status

approved