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A329299
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Numbers whose digits are in nondecreasing order in bases 9 and 10.
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7
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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
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OFFSET
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1,3
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COMMENTS
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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?
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LINKS
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EXAMPLE
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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
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MAPLE
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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:
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MATHEMATICA
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Select[Range[0, 1200], Min[Differences[IntegerDigits[#]]]>-1&& Min[ Differences[ IntegerDigits[ #, 9]]]>-1&] (* Harvey P. Dale, Oct 14 2022 *)
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CROSSREFS
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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.
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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