OFFSET
1,2
COMMENTS
From David A. Corneth, Apr 11 2024: (Start)
This sequence is well defined as A030000 is well defined; every finite string of digits is contained in some power of 2.
LINKS
Brady Haran, Apocalyptic Numbers, Numberphile video, 2024.
EXAMPLE
a(2) is the smallest k > 0 such that the digits of 2^k contain 2^a(1) = 2^1 = 2 as a proper substring, so a(2) = 5. (2^5 = 32.)
a(3) is the smallest k > 0 such that the digits of 2^k contain 2^a(2) = 32 as a proper substring, so a(3) = 15. (2^15 = 32768.)
MATHEMATICA
k = 0; Rest@ NestList[(While[SequenceCount[IntegerDigits[2^k], IntegerDigits[2^#]] == 0, k++]; k++; k - 1) &, 1, 4] (* Michael De Vlieger, Apr 19 2024 *)
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Adam Vulic, Apr 11 2024
STATUS
approved