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
KEYWORD
nonn,base
AUTHOR
Jon E. Schoenfield, Nov 17 2019
STATUS
approved