A007356 Apocalyptic powers: 2^a(n) contains 666. (Formerly M5405)

157, 192, 218, 220, 222, 224, 226, 243, 245, 247, 251, 278, 285, 286, 287, 312, 355, 361, 366, 382, 384, 390, 394, 411, 434, 443, 478, 497, 499, 506, 508, 528, 529, 539, 540, 541, 564, 578, 580, 582, 583, 610, 612, 614, 620, 624, 635, 646, 647, 648, 649, 650

Offset

1,1

Comments

Conjecture: for n > 26069, a(n) = n + 3715. [Charles R Greathouse IV, Sep 28 2011]

References

C. Pickover, Mazes for the Mind, St. Martin's Press, NY, 1992, p. 337.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Brady Haran and Tony Padilla, Apocalyptic Numbers, YouTube Numberphile video, 2024.

Eric Weisstein's World of Mathematics, Apocalyptic Number.

Example

a(1) = 157 is a term since 2^a(1) = 2^157 = 182687704666362864775460604089535377456991567872 contains 666.

Maple

q:= n-> searchtext("666", cat(2^n))>0:
select(q, [$1..1000])[];  # Alois P. Heinz, Oct 26 2019

Mathematica

Select[Range[650], SequenceCount[IntegerDigits[2^#], {6, 6, 6}]>0&] (* Harvey P. Dale, Apr 10 2022 *)

Prog

(Python)
A007356_list = [k for k in range(1000) if '666' in str(2**k)] # Chai Wah Wu, Oct 26 2019

Crossrefs

Sequence in context: A178091 A178092 A140035 * A236537 A048927 A343702

Adjacent sequences: A007353 A007354 A007355 * A007357 A007358 A007359

Keyword

base,nonn,changed

Author

N. J. A. Sloane, Simon Plouffe

Status

approved