

A316634


Numbers k such that k concatenated with k+1 and then divided by 2k+1 produces an integer after some divisions explained in the Example section.


1



1, 2, 4, 12, 13, 15, 16, 17, 20, 24, 26, 28, 32, 35, 36, 49, 60, 66, 70, 75, 76, 100, 105, 112, 119, 120, 121, 128, 132, 136, 149, 156, 159, 160, 164, 165, 166, 167, 176, 186, 207, 215, 235, 258, 266, 268, 344, 352, 356, 391, 416, 429, 499, 610, 625, 671, 675, 690, 695, 750
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OFFSET

1,2


LINKS

JeanMarc Falcoz, Table of n, a(n) for n = 1..1352


EXAMPLE

1 is in the sequence because 12/(1+2) is the integer 4;
2 is in the sequence though 23/(2+3) is not an integer, because if we do floor(23/(2+3)) we get 4, and if we use this 4 to do now 23/(2+4) we get an integer (here 4 again);
3 is not in the sequence because 34/(3+4) is not an integer and even if we try floor(34/(3+4)) = 3, we will be stuck in the loop 34/(3+4) =. . . never ending in an integer;
4 is in the sequence because 45/(4+5) is the integer 5;
5 is not in the sequence because 56/(5+6) is not an integer and even if we try floor(56/(5+6))=5, we will be stuck in the loop 56/(5+6) =. . . never ending in an integer;
. . .
13 is in the sequence though 1314/(13+14) is not an integer, but if we repeatedly apply the "floor" trick, we will produce an integer at the end (here 34): floor(1314/(13+14))= 48, then floor(1348/(13+48)) = 22, then floor(1322/(13+22)) = 37, then floor(1337/(13+37)) = 26 and finally 1326/(13+26) produces the integer 34, without the help of the "floor" function.
. . .
761 is not in the sequence because 761762/(761+762) is not an integer and even if we repeatedly apply the "floor" trick, we will be stuck in a loop: floor(761500/(761+500)) = 603, then floor(761603/(761+603)) = 558, then floor(762558/(761+558)) = 577, then floor(761577/(761+577)) = 569, then floor(761569(761+569)) = 572, then floor(761572/(761+572)) = 571, then floor(761571/(761+571)) = 571 again.
Etc.


CROSSREFS

Cf. A316534 and A316538 for other ways to concatenate/divide and iterate the procedure.
Sequence in context: A087796 A268494 A306851 * A039587 A194368 A111069
Adjacent sequences: A316631 A316632 A316633 * A316635 A316636 A316637


KEYWORD

base,nonn


AUTHOR

Eric Angelini and JeanMarc Falcoz, Jul 09 2018


STATUS

approved



