Some numbers remain numbers when turned upside down (using digits 0125689, with no final 0's): 1, 2, 5, 6, 8, 9, 11, 12, … etc

IF a₁=1, a₂=2, a₃=5,... a₈=12,…, etc

a.Evaluate a₁₀₀
b. Evaluate a₁₀₀₀
c. If a_n= 888, what is n?

valid$ = "0125689"

PRINT
FOR i = 1 TO 19000
  s$ = LTRIM$(STR$(i))
  found = 1
  FOR j = 1 TO LEN(s$)
     IF INSTR(valid$, MID$(s$, j, 1)) = 0 THEN found = 0
  NEXT
  IF RIGHT$(s$, 1) = "0" THEN found = 0
  IF found THEN
     ct = ct + 1
     IF ct < 15 OR ct = 100 OR ct = 1000 OR i = 888 THEN PRINT ct, i:
  END IF
NEXT

finds

n            a(n)
1             1
2             2
3             5
4             6
5             8
6             9
7             11
8             12
9             15
10            16
11            18
12            19
13            21
14            22
100           226
245           888
1000          5286

 

So:

a. 226
b. 5286
c. 245

The proscription on terminal zero prevents easy use of an isomorphism with base-7 numbers, where we'd just assign the valid digits to the successive base-7 digits and use base-conversion algorithms.

Posted by Charlie on 2014-04-11 15:47:31