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).

220, 222, 243, 529, 624, 648, 662, 702, 714, 838, 840, 842, 844, 846, 850, 857, 859, 867, 869, 871, 924, 925, 927, 929, 931, 975, 979, 981, 983, 1056, 1058, 1062, 1088, 1133, 1135, 1160, 1162, 1219, 1230, 1241, 1259, 1310, 1341, 1343, 1349, 1384, 1394, 1411, 1420

Offset: 1

Author

Paolo Xausa, Apr 06 2024

Keywords

• nonn
• easy
• base

Comments

A positive power of 2 containing 666 in its decimal expansion is called an apocalyptic number.

See A371806 for a variant counting only nonoverlapping substrings.

Examples

			243 is a term because 2^243 contains two (overlapping) 666 substrings in its decimal expansion:
.
                   ***
14134776518227074636666380005943348126619871175004951664972849610340958208.
                    ***
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Brady Haran and Tony Padilla, Apocalyptic Numbers, YouTube Numberphile video, 2024.
• Eric Weisstein's World of Mathematics, Apocalyptic Number.

Crossrefs

Subsequence of A007356.

Cf. A371806, A371809.

Programs

Mathematica

Select[Range[2000], StringCount[IntegerString[2^#], "666", Overlaps->True] > 1 &]

Python

def ok(n): return (s:=str(1< 1 or "6666" in s
print([k for k in range(2000) if ok(k)]) # Michael S. Branicky, Apr 07 2024