A309617 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.

113, 216, 319, 4113, 5117, 6221, 7225, 8329, 9333, 10338, 11343, 12348, 13353, 14358, 15363, 16368, 17373, 18378, 19383, 20388, 21393, 22398, 233104, 243110, 253116, 263122, 273128, 283134, 293140, 303146, 313152, 323158, 333164, 343170, 353176, 363182, 373188, 383194, 393200, 403206, 413212, 423218, 433224, 443230, 453236

Offset

1,1

Comments

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.

Links

Carole Dubois, Table of n, a(n) for n = 1..1002

Carole Dubois, graph with axe Y logarithmic

Example

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;
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;
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;
...
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);
etc.

Crossrefs

Sequence in context: A054695 A054696 A142426 * A210512 A319936 A142700

Adjacent sequences: A309614 A309615 A309616 * A309618 A309619 A309620

Keyword

nonn,base

Author

Eric Angelini and Carole Dubois, Aug 10 2019

Status

approved