A379140 Numbers k such that the greatest prime < 10^k and the least prime > 10^k share no decimal digits.

1, 2, 8, 11, 15, 16, 17, 18, 21, 25, 26, 30, 40, 44, 46, 47, 50, 51, 53, 55, 60, 63, 64, 74, 77, 81, 86, 88, 89, 93, 95, 101, 123, 130, 131, 133, 134, 140, 152, 154, 158, 161, 164, 166, 176, 181, 189, 192, 198, 209, 214, 215, 233, 245, 264, 268, 274, 291, 293, 295, 297, 324, 326, 334, 352, 357

Offset

1,2

Comments

Charles R Greathouse IV conjectures that A107801(n) = prime(n) for n sufficiently large (and similarly for other related sequences). If that is the case, this sequence must be finite.

Links

Robert Israel, Table of n, a(n) for n = 1..250

Example

a(3) = 8 is a term because the greatest prime < 10^8 and the least prime > 10^8 are 99999989 and 100000007 respectively, and these have no digits in common.
5 is not a term because the greatest prime < 10^5 and the least prime > 10^5 are 99991 and 100003 respectively, and these have digit 1 in common.

Maple

filter:= t -> convert(convert(prevprime(10^t), base, 10), set) intersect convert(convert(nextprime(10^t), base, 10), set) = {}:
select(filter, [$1..400]);

Crossrefs

Cf. A003617, A003618, A107801.

Sequence in context: A297831 A045086 A366915 * A064105 A129516 A220269

Adjacent sequences: A379137 A379138 A379139 * A379141 A379142 A379143

Keyword

nonn,base

Author

Robert Israel, Dec 16 2024

Status

approved