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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 2 09:22 EDT 2021. Contains 346422 sequences. (Running on oeis4.)