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A266568 a(n) = smallest k such that 2^k ends in a string of exactly n nonzero digits. 0
0, 4, 7, 13, 14, 18, 50, 24, 27, 31, 34, 37, 68, 93, 49, 51, 116, 214, 131, 155, 67, 72, 76, 77, 81, 86, 149, 498, 154, 286, 359, 866, 1225, 329, 664, 129, 573, 176, 655, 820, 571, 434, 1380, 475, 1260, 2251, 6015, 3066, 1738, 2136, 2297, 432, 665, 229, 1899 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Since 2^a(n) must have at least n digits, a(n) >= (n-1)*log_2(10).

The 26-digit number 2^86 = 77371252455336267181195264 is almost certainly the largest power of 2 that contains no zero digit.

A notably low local minimum occurs at a(36) = 129, which is less than a(n) for all n > 26.

A notably high local maximum occurs at a(122) = 11267047.

LINKS

Table of n, a(n) for n=1..55.

EXAMPLE

2^0 = 1 is the smallest power of 2 ending in a string ("1") of exactly 1 nonzero digit, so a(1) = 0.

2^4 = 16 is the smallest power of 2 ending in a string ("16") of exactly 2 nonzero digits, so a(2) = 4.

2^50 = 1125899906842624 is the smallest power of 2 ending in a string ("6842624") of exactly 7 nonzero digits, so a(7) = 50.

The last 7 digits of 2^24 = 16777216 -- i.e., "6777216" -- are also nonzero, but so is the preceding digit, so 2^24 ends in a string of exactly 8 nonzero digits. Since no smaller power of 2 ends in exactly 8 nonzero digits, a(8) = 24.

CROSSREFS

Cf. A007377, A031140, A031141, A031142, A031143, A181611.

Sequence in context: A283626 A184864 A031142 * A244436 A310794 A310795

Adjacent sequences:  A266565 A266566 A266567 * A266569 A266570 A266571

KEYWORD

nonn,base

AUTHOR

Jon E. Schoenfield, Jan 01 2016

STATUS

approved

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Last modified November 18 01:41 EST 2019. Contains 329242 sequences. (Running on oeis4.)