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

Author

Klaus Brockhaus, Aug 30 2005

Keywords

• nonn
• base
• more

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

Examples

			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.
		

Links

• Patrick De Geest, The Nine Digits Page
• Eric Weisstein's World of Mathematics, Pandigital

Crossrefs

Cf. A089081 (26th powers).

Programs

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

Extensions

a(28) from Lars Blomberg, Sep 25 2011