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

Author

Robert Israel, Dec 16 2024

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A003617, A003618, A107801.

Programs

Maple

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