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

1,2

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).

Links

Table of n, a(n) for n=1..25.

Example

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

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}]]

Crossrefs

Sequence in context: A165138 A196395 A358380 * A070919 A070847 A195863

Adjacent sequences: A139123 A139124 A139125 * A139127 A139128 A139129

Keyword

base,nonn

Author

T. D. Noe, Apr 08 2008

Status

approved