Find a 13 digit positive integer N whose base ten representation consists entirely of 8s and 9s such that 2¹³ divides N.

DECLARE SUB vary (psn#)
DEFDBL A-Z
DIM SHARED bse
bse = 8888888888888#
vary 0

SUB vary (psn)
 addend = INT(10 ^ psn + .5)
 modval = bse
 q = INT(bse / 8192)
 r = bse - q * 8192
 IF r = 0 THEN PRINT bse
 IF psn < 12 THEN vary psn + 1
 bse = bse + addend
 modval = bse
 q = INT(bse / 8192)
 r = bse - q * 8192
 IF r = 0 THEN PRINT bse
 IF psn < 12 THEN vary psn + 1
 bse = bse - addend
END SUB

gives

8898989989888

Posted by Charlie on 2011-12-21 12:41:17