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

1,1

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.

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.

Example

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

Mathematica

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

Prog

(Python)
def ok(n): return (s:=str(1<<n)).count("666") > 1 or "6666" in s
print([k for k in range(2000) if ok(k)]) # Michael S. Branicky, Apr 07 2024

Crossrefs

Subsequence of A007356.

Cf. A371806, A371809.

Sequence in context: A157645 A157673 A064477 * A371806 A217160 A203777

Adjacent sequences: A371805 A371806 A371807 * A371809 A371810 A371811

Keyword

nonn,easy,base

Author

Paolo Xausa, Apr 06 2024

Status

approved