A139126 Least k such that the last n decimal digits of 2^k are all powers of 2.

0, 7, 7, 18, 19, 90, 91, 271, 1751, 18807, 56589, 56589, 56589, 56589, 899791, 899791, 2814790, 7635171, 7635171, 39727671, 99530619, 233093807, 233093807, 233093807, 233093807

Offset: 1

Author

T. D. Noe, Apr 08 2008

Keywords

• base
• nonn

Comments

Does k exist for all n? This sequence is inspired by A130693, which lists all known powers of 2 whose digits are all powers of 2 (that is, 1, 2, 4, or 8).

Examples

			2^19=524288 is the least power of 2 ending with 5 digits that are powers of 2.
		

Programs

Mathematica

k=1; Join[{0}, Table[k--; pwr=PowerMod[2,k,10^n]; While[k++; pwr=Mod[2*pwr,10^n]; d=Union[IntegerDigits[pwr,10,n]]; Intersection[d,{3,5,6,7,9,0}]!={}]; k, {n,2,10}]]