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

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

Examples

			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.
		

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 and of A371808.

Cf. A371807.

Programs

Mathematica

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

Python

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