OEIS A212558: Proof of Unproven Conjecture? Proven!
12-18-2017, 10:27 AM
Post: #4
 Paul Dale Senior Member Posts: 1,758 Joined: Dec 2013
RE: OEIS A212558: Proof of Unproven Conjecture?
The same property seems to hold for other bases apart from 10:

Code:
 BS  MAXn Native  2   255 11111111  3   485 122222  4   767 23333  5   624 4444  6   295 5555  7  2057 5666  8  2047 3777  9  2915 3888 10  2999 2999 11  3992 2aaa 12  3455 1bbb 13  4393 1ccc 14  5487 1ddd 15  6749 1eee 16  8191 1fff 17  4912 ggg 18  5831 hhh 19  6858 iii 20  7999 jjj 21  9260 kkk 22 10647 lll 23 12166 mmm 24 13823 nnn 25 15624 ooo 26 17575 ppp 27 19682 qqq 28 21951 rrr 29 24388 sss 30 26999 ttt 31 29790 uuu 32 32767 vvv 33 35936 www 34 39303 xxx 35 39199 vyy 36 38879 tzz

BS is the base, MAXn is the largest n for which a(n) is non-zero. Native is n presented in the specified base rather than base 10.

Some observations:
• The final digits are always a run of the highest digit permitted in the base.
• The binary bases apart from four (2, 8, 16, 32) are equivalent to a run of set bits in binary (no gaps). Why is base 4 special?
• The sequence is generally increasing but dips between bases 16 and 17.

It is interesting to note that the final number always ends with a run of the largest digit permitted by the base.
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 Messages In This Thread OEIS A212558: Proof of Unproven Conjecture? Proven! - Gerald H - 12-18-2017, 08:23 AM RE: OEIS A212558: Proof of Unproven Conjecture? - pier4r - 12-18-2017, 08:26 AM RE: OEIS A212558: Proof of Unproven Conjecture? - stored - 12-18-2017, 10:21 AM RE: OEIS A212558: Proof of Unproven Conjecture? - Gerald H - 12-18-2017, 12:00 PM RE: OEIS A212558: Proof of Unproven Conjecture? - Paul Dale - 12-18-2017 10:27 AM RE: OEIS A212558: Proof of Unproven Conjecture? - Gerald H - 12-18-2017, 01:29 PM RE: OEIS A212558: Proof of Unproven Conjecture? Proven! - Paul Dale - 12-18-2017, 10:22 PM RE: OEIS A212558: Proof of Unproven Conjecture? Proven! - Gerald H - 12-19-2017, 05:39 AM RE: OEIS A212558: Proof of Unproven Conjecture? Proven! - stored - 12-19-2017, 06:21 AM RE: OEIS A212558: Proof of Unproven Conjecture? Proven! - Gerald H - 12-19-2017, 08:10 AM

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