A165411 Primes p such that each of p's digits d appears consecutively exactly d times and p contains each nonzero digit up to its maximum digit.

223331, 122555554444333, 224444333555551, 224444555553331, 225555544441333, 333555554444221, 555552233344441, 555552244441333, 555554444221333, 122444455555666666333, 122555554444666666333, 144446666662255555333

Offset: 1

Author

Rick L. Shepherd, Sep 17 2009

Keywords

• base
• easy
• fini
• full
• nonn

Comments

This sequence is a subsequence of A140057, A078348, and A108571. There are 129 terms; the largest is 7777777666666444455555223331. As 1, 122, and 221 are not prime and any such numbers whose maximum digit is 4, 8, or 9 are divisible by 3, all terms of the sequence have either 6 (1 term), 15 (8 terms), 21 (24 terms), or 28 (96 terms) decimal digits (=triangular numbers A000217(n) for n=3,5,6,7, respectively).

None of the terms have nondecreasing or nonincreasing decimal digits. - Rick L. Shepherd, Feb 23 2013

Examples

			1333444455555226666667777777 is a term because it is a prime meeting the criteria: It contains all digits 1 through 7, its maximum, each appearing in a single run of length equal to the value of the digit.
		

Links

• Rick L. Shepherd, Table of n, a(n) for n = 1..129 (full sequence)

Crossrefs

Cf. A140057, A078348, A108571.