login
A371806
Exponents k > 0 of powers of 2 such that the decimal expansion of 2^k contains more than one nonoverlapping 666 substring.
3
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
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
KEYWORD
nonn,easy,base
AUTHOR
Paolo Xausa, Apr 06 2024
STATUS
approved