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A300102
Smallest prime containing exactly n consecutive 0's.
1
2, 101, 1009, 10007, 100003, 1000003, 20000003, 100000007, 1000000007, 30000000001, 100000000003, 2000000000003, 40000000000001, 1000000000000037, 6000000000000001, 20000000000000003, 100000000000000003, 1000000000000000003, 60000000000000000007, 500000000000000000003
OFFSET
0,1
COMMENTS
Sequence agrees with A037053 up to a(31) (see comment in A037053). A269230 lists indices where these 2 sequences differ.
For the first 1001 terms of this sequence, the number of nonzero digits of each term is 4 or less. This differs from A037053 for which the number of nonzero digits is 3 or less for the first 12000 terms. Does there exist n such that a(n) has 5 or more nonzero digits?
a(n) has 3 nonzero digits for n = 13, 22, 29, 31, 32, 33, 40, 42, 43, ...
a(n) has 4 nonzero digits for n = 192, 213, 238, 250, 252, 257, 268, 293, 297, 303, ...
a(n) <> A037053(n) and a(n) = A037053(m) for some m > n for n = 436, 780, 845, 866, 894, 911, 945, 957, 967, ... In all these cases so far, a(n) has n+1 zero digits. Are there n satisfying these conditions such that a(n) has more than n+1 zero digits?
Sequence is not monotonically increasing; indices for which a(n) > a(n+1) are 22, 43, 47, 58, 67, 105, 108, 121, 132, 144, 192, 220, 238, 250, 252, 257, 261, 270, ...
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Chai Wah Wu, Feb 25 2018
STATUS
approved