A371807 Number of nonoverlapping 666 substrings contained in the decimal expansion of the n-th apocalyptic number.

1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2

Offset

1,4

Comments

An apocalyptic number is a positive power of 2 containing 666 in its decimal expansion.

See A371809 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.

Formula

a(n) <= A371809(n).

Example

a(4) = 2 because the 4th apocalyptic number (2^220) contains two nonoverlapping 666 substrings in its decimal expansion:
2^220 = 168499(666)66969149871(666)88442938726917102321526408785780068975640576.

Mathematica

Select[StringCount[IntegerString[2^Range[1000]], "666"], # > 0 &]

Prog

(Python)
from itertools import islice
def agen(): # generator of terms
    pow2 = 1
    while True:
        s = str(pow2)
        if (c := s.count("666")) > 0: yield c
        pow2 <<= 1
print(list(islice(agen(), 88))) # Michael S. Branicky, Apr 07 2024

Crossrefs

Cf. A007356, A371806, A371809.

Sequence in context: A085978 A141044 A064284 * A370975 A030409 A030407

Adjacent sequences: A371804 A371805 A371806 * A371808 A371809 A371810

Keyword

nonn,easy,base

Author

Paolo Xausa, Apr 06 2024

Status

approved