A247045 Triangle read by rows: T(n,k) = least number m > 0 such that m^k in base n contains exactly k distinct digits, 1 <= k <= n.

1, 1, 2, 1, 3, 4, 1, 2, 3, 5, 1, 3, 3, 6, 12, 1, 3, 5, 7, 7, 15, 1, 3, 5, 9, 5, 17, 15, 1, 4, 5, 10, 9, 7, 11, 33, 1, 3, 5, 7, 11, 19, 14, 16, 53, 1, 4, 5, 6, 7, 13, 13, 14, 21, 36, 1, 4, 5, 7, 10, 8, 12, 12, 16, 42, 41, 1, 4, 6, 16, 11, 8, 19, 19, 16, 28, 35, 55, 1, 4, 6, 9, 9, 14, 10, 18, 14

Offset: 1

Author

Derek Orr, Sep 10 2014

Keywords

• nonn
• base
• tabl

Examples

			T(n,k) is given by (row n corresponds to base n):
1;
1, 2;
1, 3, 4;
1, 2, 3,  5;
1, 3, 3,  6, 12;
1, 3, 5,  7,  7, 15;
1, 3, 5,  9,  5, 17, 15;
1, 4, 5, 10,  9,  7, 11, 33;
1, 3, 5,  7, 11, 19, 14, 16, 53;
1, 4, 5,  6,  7, 13, 13, 14, 21, 36; (base 10)
1, 4, 5,  7, 10,  8, 12, 12, 16, 42, 41;
Example: T(7,3) = 5 means that 5 is the smallest number such that 5^3 in base 7 (which is 125 in base 7 = 236) has 3 distinct digits (2, 3, and 6).
		

Links

• Indranil Ghosh, Rows 1..36 of triangle, flattened

Crossrefs

Cf. A016069, A155146, A155150.

Programs

PARI

print1(1,", ");n=2;while(n<20,m=1;for(k=1,n,while(m,d=digits(m^k,n);if(#vecsort(d,,8)!=k,m++);if(#vecsort(d,,8)==k,print1(m,", ");m=1;break)));n++)