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A139126
Least k such that the last n decimal digits of 2^k are all powers of 2.
0
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).
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
KEYWORD
base,nonn
AUTHOR
T. D. Noe, Apr 08 2008
STATUS
approved