login
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
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?
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
MATHEMATICA
Select[Range[0, 1200], Min[Differences[IntegerDigits[#]]]>-1&& Min[ Differences[ IntegerDigits[ #, 9]]]>-1&] (* Harvey P. Dale, Oct 14 2022 *)
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 A365127
KEYWORD
nonn,base
AUTHOR
Jon E. Schoenfield, Nov 17 2019
STATUS
approved