OFFSET
1,1
COMMENTS
Numbers of the form concat(92,(10^k - 1)/9) and concat(69,4*(10^k - 1)/9,6) for k>0 are part of the sequence.
The first digit of a term must be 5 or higher. Numbers of the form 925925...92592 are terms, i.e. concatenate 925 m times for m >= 0 and append 92. Numbers of the form concat(2*(10^k-1)/3,9,(10^(k-1)-1)/3,4,2*(10^k-1)/3) for k > 1 are also terms. It also works for the case k=1 if the middle 0 that results is removed. If a term n is even, then the digits of n besides the least significant digit must contain either 4 or 9. If a term n is odd and not divisible by 5, then the digits of n besides the least significant digit must contain 9. - Chai Wah Wu, May 10 2017
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..51
EXAMPLE
75 = concat(7,5) and 7 * 5 = 35 is the 10’s complement of 75.
584799 = concat(58479,9) and 58479 * 9 = 526311 is the 10’s complement of 584799.
7694443 = concat(769,4443) and 769 * 4443 = 3416667 is the 10’s complement of 7694443.
MAPLE
P:=proc(q) local a, b, c, d, k, ok, n; for n from 1 to q do b:=ilog10(n)+1; c:=n; ok:=1;
d:=0; for k from 1 to b do if (c mod 10)>0 then a:=(10-(c mod 10)); d:=d+10^(k-1)*a; c:=trunc(c/10); else ok:=0; break; fi; od; if ok=1 then for k from 1 to b do
if d=(n mod 10^k)*trunc(n/10^k) then print(n); fi; od; fi; od; end: P(10^7);
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, May 08 2017
STATUS
approved