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A329299 Numbers whose digits are in nondecreasing order in bases 9 and 10. 7
0, 1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14, 15, 16, 17, 22, 23, 24, 25, 26, 33, 34, 35, 44, 111, 112, 113, 114, 115, 116, 122, 123, 124, 125, 133, 134, 188, 222, 223, 224, 233, 277, 278, 366, 367, 368, 377, 455, 456, 457, 458, 466, 467, 556, 557, 566, 1113 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(91) = 12555566 is the largest term < 10^10000 (which is a 10480-digit number in base 9). But can it be proved that 12555566 is the final term of the sequence?

LINKS

Table of n, a(n) for n=1..58.

EXAMPLE

Sequence includes, respectively, 9, 16, 32, and 11 terms that are 1-, 2-, 3-, and 4- digit terms in both bases, and the following:

  a(69) =    14777 =    22238_9

  a(70) =    15677 =    23448_9

  a(71) =    22234 =    33444_9

  a(72) =    22235 =    33445_9

  a(73) =    22236 =    33446_9

  a(74) =    22237 =    33447_9

  a(75) =    22238 =    33448_9

  a(76) =    22244 =    33455_9

  a(77) =    22245 =    33456_9

  a(78) =    22246 =    33457_9

  a(79) =    22247 =    33458_9

  a(80) =    22255 =    33467_9

  a(81) =    22256 =    33468_9

  a(82) =    22335 =    33566_9

  a(83) =    22336 =    33567_9

  a(84) =    22337 =    33568_9

  a(85) =    22345 =    33577_9

  a(86) =    22346 =    33578_9

  a(87) =    22355 =    33588_9

  a(88) =    44468 =    66888_9

  a(89) =   222344 =   367888_9

  a(90) =  1233467 =  2278888_9

  a(91) = 12555566 = 25555888_9

MAPLE

filter:= proc(n) local L;

  L:= convert(n, base, 10);

  `and`(seq(L[i+1]<=L[i], i=1..nops(L)-1))

end proc:

ND[1]:= [$1..8]: R:= $0..8:

for d from 2 to 10 do

  ND[d]:= map(t -> seq(9*t+r, r=(t mod 9) ..8), ND[d-1]);

  R:= R, op(select(filter, ND[d]));

od:

R; # Robert Israel, Nov 20 2019

CROSSREFS

Intersection of A023751 (base 9) and A009994 (base 10). Numbers whose digits are in nondecreasing order in bases b and b+1: A329294 (b=4), A329295 (b=5), A329296 (b=6), A329297 (b=7), A329299 (b=8), this sequence (b=9). See A329300 for the (apparently) largest term of each of these sequences.

Sequence in context: A032880 A032847 A023778 * A173016 A053577 A093515

Adjacent sequences:  A329296 A329297 A329298 * A329300 A329301 A329302

KEYWORD

nonn,base

AUTHOR

Jon E. Schoenfield, Nov 17 2019

STATUS

approved

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Last modified July 15 00:36 EDT 2020. Contains 335762 sequences. (Running on oeis4.)