A371806 Exponents k > 0 of powers of 2 such that the decimal expansion of 2^k contains more than one nonoverlapping 666 substring.

220, 222, 529, 624, 648, 702, 714, 844, 846, 850, 859, 924, 925, 929, 931, 979, 981, 983, 1062, 1088, 1133, 1135, 1219, 1230, 1241, 1259, 1310, 1343, 1349, 1384, 1394, 1467, 1472, 1495, 1503, 1524, 1550, 1589, 1627, 1631, 1642, 1652, 1656, 1663, 1679, 1744, 1751

Offset

1,1

Comments

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

See A371808 for a variant where overlapping substrings are counted as distinct.

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

220 is a term because 2^220 contains more than one nonoverlapping 666 substring in its decimal expansion:
2^220 = 168499(666)66969149871(666)88442938726917102321526408785780068975640576.

Mathematica

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

Prog

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

Crossrefs

Subsequence of A007356 and of A371808.

Cf. A371807.

Sequence in context: A157673 A064477 A371808 * A217160 A203777 A274116

Adjacent sequences: A371803 A371804 A371805 * A371807 A371808 A371809

Keyword

nonn,easy,base

Author

Paolo Xausa, Apr 06 2024

Status

approved