%I
%S 113,216,319,4113,5117,6221,7225,8329,9333,10338,11343,12348,13353,
%T 14358,15363,16368,17373,18378,19383,20388,21393,22398,233104,243110,
%U 253116,263122,273128,283134,293140,303146,313152,323158,333164,343170,353176,363182,373188,383194,393200,403206,413212,423218,433224,443230,453236
%N Integers that concatenate 3 counts: the number of terms in the sequence so far, the number of primes in the sequence so far, the number of digits in the sequence so far, with a(1)= 113. The sequence is always extended with the smallest available integer not leading to a contradiction or a dead end.
%C What would a dead end be? We have here a(8) = 8329 though a(8) = 8229 is sound (and lexicographically better); but 8229 brings the sequence to an end after a(9) = 9233 and a(10) = 10238 (indeed, 10238 can't be followed by anything without a contradiction). It is unknown by the authors if this sequence is finite or not.
%H Carole Dubois, <a href="/A309617/b309617.txt">Table of n, a(n) for n = 1..1002</a>
%H Carole Dubois, <a href="/A309617/a309617.jpg">graph with axe Y logarithmic</a>
%e a(1) = 113 must be read like this: "so far in the sequence there are 1 integer, 1 prime and 3 digits", which is true;
%e a(2) = 216 must be read like this: "so far in the sequence there are 2 integers, 1 prime and 6 digits", which is true;
%e a(3) = 319 must be read like this: "so far in the sequence there are 3 integers, 1 prime and 9 digits", which is true;
%e ...
%e a(6) = 6221 must be read like this: "so far in the sequence there are 6 integers, 2 primes and 21 digits", which is true (the 2 primes are 113 and 6221 itself);
%e etc.
%K nonn,base
%O 1,1
%A _Eric Angelini_ and _Carole Dubois_, Aug 10 2019
