cp's OEIS Frontend

A371808 Exponents k > 0 of powers of 2 such that the decimal expansion of 2^k contains more than one 666 substring (overlapping substrings are counted as distinct).

%I A371808 #26 Feb 16 2025 08:34:06
%S A371808 220,222,243,529,624,648,662,702,714,838,840,842,844,846,850,857,859,
%T A371808 867,869,871,924,925,927,929,931,975,979,981,983,1056,1058,1062,1088,
%U A371808 1133,1135,1160,1162,1219,1230,1241,1259,1310,1341,1343,1349,1384,1394,1411,1420
%N A371808 Exponents k > 0 of powers of 2 such that the decimal expansion of 2^k contains more than one 666 substring (overlapping substrings are counted as distinct).
%C A371808 A positive power of 2 containing 666 in its decimal expansion is called an apocalyptic number.
%C A371808 See A371806 for a variant counting only nonoverlapping substrings.
%H A371808 Paolo Xausa, <a href="/A371808/b371808.txt">Table of n, a(n) for n = 1..10000</a>
%H A371808 Brady Haran and Tony Padilla, <a href="https://www.youtube.com/watch?v=0LkBwCSMsX4">Apocalyptic Numbers</a>, YouTube Numberphile video, 2024.
%H A371808 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ApocalypticNumber.html">Apocalyptic Number</a>.
%e A371808 243 is a term because 2^243 contains two (overlapping) 666 substrings in its decimal expansion:
%e A371808 .
%e A371808                    ***
%e A371808 14134776518227074636666380005943348126619871175004951664972849610340958208.
%e A371808                     ***
%t A371808 Select[Range[2000], StringCount[IntegerString[2^#], "666", Overlaps->True] > 1 &]
%o A371808 (Python)
%o A371808 def ok(n): return (s:=str(1<<n)).count("666") > 1 or "6666" in s
%o A371808 print([k for k in range(2000) if ok(k)]) # _Michael S. Branicky_, Apr 07 2024
%Y A371808 Subsequence of A007356.
%Y A371808 Cf. A371806, A371809.
%K A371808 nonn,easy,base
%O A371808 1,1
%A A371808 _Paolo Xausa_, Apr 06 2024