This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A371806 #29 Feb 16 2025 08:34:06
%S A371806 220,222,529,624,648,702,714,844,846,850,859,924,925,929,931,979,981,
%T A371806 983,1062,1088,1133,1135,1219,1230,1241,1259,1310,1343,1349,1384,1394,
%U A371806 1467,1472,1495,1503,1524,1550,1589,1627,1631,1642,1652,1656,1663,1679,1744,1751
%N A371806 Exponents k > 0 of powers of 2 such that the decimal expansion of 2^k contains more than one nonoverlapping 666 substring.
%C A371806 A positive power of 2 containing 666 in its decimal expansion is called an apocalyptic number.
%C A371806 See A371808 for a variant where overlapping substrings are counted as distinct.
%H A371806 Paolo Xausa, <a href="/A371806/b371806.txt">Table of n, a(n) for n = 1..10000</a>
%H A371806 Brady Haran and Tony Padilla, <a href="https://www.youtube.com/watch?v=0LkBwCSMsX4">Apocalyptic Numbers</a>, YouTube Numberphile video, 2024.
%H A371806 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ApocalypticNumber.html">Apocalyptic Number</a>.
%e A371806 220 is a term because 2^220 contains more than one nonoverlapping 666 substring in its decimal expansion:
%e A371806 2^220 = 168499(666)66969149871(666)88442938726917102321526408785780068975640576.
%t A371806 Select[Range[2000], StringCount[IntegerString[2^#], "666"] > 1 &]
%o A371806 (Python)
%o A371806 def ok(n): return str(1<<n).count("666") > 1
%o A371806 print([k for k in range(2000) if ok(k)]) # _Michael S. Branicky_, Apr 07 2024
%Y A371806 Subsequence of A007356 and of A371808.
%Y A371806 Cf. A371807.
%K A371806 nonn,easy,base
%O A371806 1,1
%A A371806 _Paolo Xausa_, Apr 06 2024