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A308527 Numbers that, for some x, are the concatenation of x+2, x+1 and x and are divisible by at least two of x+2, x+1 and x. 2
321, 432, 121110, 171615, 343332, 118117116, 232231230, 334333332, 333433333332, 452245214520, 333343333333332, 333334333333333332, 333333433333333333332, 333333343333333333333332 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
For each d>=1, (10^(3*d)-4)/3+10^(2*d) (the concatenation of x+2, x+1 and x where x = (10^d-4)/3) is in the sequence, being divisible by x+1 and x+3. Thus the sequence is infinite.
It appears that a(n) is of the form (10^(3*d)-4)/3+10^(2*d) for n >= 11. - Chai Wah Wu, Jun 19 2019
LINKS
EXAMPLE
232231230 is the concatenation of 232, 231 and 230, and is divisible by 231 and 230, so it is in the sequence.
MAPLE
f:= proc(x)
local t1, t2, q, a, b;
t1:= 10^length(x);
t2:= t1*10^length(x+1);
q:= x*(1+t1+t2)+2*t2+t1;
a:= (q/x)::integer;
b:= (q/(x+1))::integer;
if a and b then return q elif not(a) and not(b) then return NULL fi;
if (q/(x+2))::integer then q else NULL fi
end proc:
map(f, [$1..10^8]);
CROSSREFS
Cf. A306643.
Subsequence of A127424.
Sequence in context: A300849 A351994 A261262 * A268517 A228226 A004927
KEYWORD
nonn,base
AUTHOR
J. M. Bergot and Robert Israel, Jun 05 2019
STATUS
approved

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Last modified June 9 00:10 EDT 2023. Contains 363165 sequences. (Running on oeis4.)