A300102 Smallest prime containing exactly n consecutive 0's.

2, 101, 1009, 10007, 100003, 1000003, 20000003, 100000007, 1000000007, 30000000001, 100000000003, 2000000000003, 40000000000001, 1000000000000037, 6000000000000001, 20000000000000003, 100000000000000003, 1000000000000000003, 60000000000000000007, 500000000000000000003

Offset: 0

Author

Chai Wah Wu, Feb 25 2018

Keywords

• nonn
• base

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, ...

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A037053, A269230, A269260.