666 and godly numbers

[Joshua Zucker]

On Tue, Mar 4, 2008 at 6:27 AM, Maximilian Hasler
<maximilian.hasler at gmail.com> wrote:
>  So one should think about an alternate definition (easiest:
>  "ungodly"(?) numbers, a supersequence of
>  A121205 : "666" in bases 7 and higher rewritten in base 10.

OK, I computed all terms less than 100000 for this "ungodly" sequence
and submitted them to OEIS just now.  Below I made this message
shorter by stopping at 10000 (so the below is a subset of my
submission to OEIS).  I hope Max&Maximilian are OK with my giving
credit as in the below; if not please let me know how you'd like me to
rewrite the submission.

--Joshua

%I A000001
%S A000001 342 438 546 666 685 798 942 950 1028 1098 1266 1275 1371
1446 1462 1638 1666 1714 1842 1974 2004 2057 2058 2129 2286 2394 2395
2396 2397 2398 2399 2400 2486 2526 2666 2670 2733 2743 2778 2998 3042
3086 3295 3318 3429 3460 3462 3504 3505 3506 3507 3508 3509 3510 3511
3606 3666 3772 3906 4010 4022 4115 4191 4218 4398 4458 4534 4542 4666
4791 4795 4796 4797 4798 4799 4800 4801 4821 4878 4914 4915 4916 4917
4918 4919 4920 4921 4922 5046 5144 5226 5487 5492 5558 5586 5649 5666
5734 5830 5958 6070 6122 6126 6173 6342 6378 6516 6582 6660 6661 6662
6663 6664 6665 6666 6667 6668 6669 6738 6754 6755 6859 7094 7107 7146
7196 7197 7198 7199 7200 7201 7202 7453 7545 7566 7600 7601 7602 7603
7604 7605 7606 7607 7666 7689 7836 7854 7888 7890 7998 8118 8196 8231
8442 8565 8574 8630 8666 8778 8779 8780 8781 8782 8783 8784 8785 8786
8787 8788 8898 8917 9142 9145 9260 9294 9366 9498 9582 9597 9598 9599
9600 9601 9602 9603 9654 9666 9830 9846 9886 9946
%N A000001 "Ungodly" numbers: numbers that, in some base b>6, contain
the string 666 at least once in their expansion.
%C A000001 Max Alekseyev asked if there are an infinite amount of
godly numbers.  Maximilian Hasler pointed out that up to the length in
OEIS, the godly numbers would just look like the integers, and
suggested submitting the ungodly numbers.
%e A000001 342 is in the sequence because 342 = 666 base 7.  685 is in
the sequence because 685 = 1666 in base 7.  99968 is in the sequence
because 99968 = 3666B in base 13.
%Y A000001 A121205 is the numbers that in some base b are represented
exactly as 666, so is a subsequence of this sequence.
%O A000001 1
%K A000001 ,base,nonn,
%A A000001 Joshua Zucker (joshua.zucker at stanfordalumni.org), Mar 04 2008