A number of the form 2ⁿ is called apocalyptic if its digits contain "666" as a substring.

Find the smallest apocalyptic number.

Helpful hints:
1. n is below 200.
2. n is below 250 for two appearances.
3. below 1000 for three.

The smallest apocalyptic number of the form 2ⁿ is the 48-digit number equal to 2¹⁵⁷.


2¹⁵⁷=182687704666362864775460604089535377456991567872

Note: It is assumed that the number of sequences of "666" in the number's long form excludes the counts where one of the digits are already included in a sequence already counted. 

2²²⁰=1684996666696914987166688442938726917102321526408785780068975640576

2⁹³¹=18152061871066687778296661354368903321914797383537530017770652579540291225102592450502542901564408576535628952517004065557306948798155587253306037366972590646764780767180906664339433713797579795779287057890032192456881698082005372169886461674177955114893128728688280185836979355648

Edited on November 11, 2017, 9:40 am

Posted by Dej Mar on 2017-11-11 09:19:40