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A371807 Number of nonoverlapping 666 substrings contained in the decimal expansion of the n-th apocalyptic number.

%I A371807 #22 Feb 16 2025 08:34:06
%S A371807 1,1,1,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,
%T A371807 1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,1,
%U A371807 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2
%N A371807 Number of nonoverlapping 666 substrings contained in the decimal expansion of the n-th apocalyptic number.
%C A371807 An apocalyptic number is a positive power of 2 containing 666 in its decimal expansion.
%C A371807 See A371809 for a variant where overlapping substrings are counted as distinct.
%H A371807 Paolo Xausa, <a href="/A371807/b371807.txt">Table of n, a(n) for n = 1..10000</a>
%H A371807 Brady Haran and Tony Padilla, <a href="https://www.youtube.com/watch?v=0LkBwCSMsX4">Apocalyptic Numbers</a>, YouTube Numberphile video, 2024.
%H A371807 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ApocalypticNumber.html">Apocalyptic Number</a>.
%F A371807 a(n) <= A371809(n).
%e A371807 a(4) = 2 because the 4th apocalyptic number (2^220) contains two nonoverlapping 666 substrings in its decimal expansion:
%e A371807 2^220 = 168499(666)66969149871(666)88442938726917102321526408785780068975640576.
%t A371807 Select[StringCount[IntegerString[2^Range[1000]], "666"], # > 0 &]
%o A371807 (Python)
%o A371807 from itertools import islice
%o A371807 def agen(): # generator of terms
%o A371807     pow2 = 1
%o A371807     while True:
%o A371807         s = str(pow2)
%o A371807         if (c := s.count("666")) > 0: yield c
%o A371807         pow2 <<= 1
%o A371807 print(list(islice(agen(), 88))) # _Michael S. Branicky_, Apr 07 2024
%Y A371807 Cf. A007356, A371806, A371809.
%K A371807 nonn,easy,base
%O A371807 1,4
%A A371807 _Paolo Xausa_, Apr 06 2024