A165411 - OEIS

%I #6 Feb 23 2013 21:03:16

%S 223331,122555554444333,224444333555551,224444555553331,

%T 225555544441333,333555554444221,555552233344441,555552244441333,

%U 555554444221333,122444455555666666333,122555554444666666333,144446666662255555333

%N 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.

%C 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).

%C None of the terms have nondecreasing or nonincreasing decimal digits. - _Rick L. Shepherd_, Feb 23 2013

%H Rick L. Shepherd, <a href="/A165411/b165411.txt">Table of n, a(n) for n = 1..129</a> (full sequence)

%e 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.

%Y Cf. A140057, A078348, A108571.

%K base,easy,fini,full,nonn

%O 1,1

%A _Rick L. Shepherd_, Sep 17 2009