Self Champernowne Erase

Self-erasing Champernowne’s decimal expansion

We explain here how http://www.research.att.com/~njas/sequences/A108668 was build:

01234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465666768697071727374757677787980

[Sean Irvine, (Friday, August 13^th, 2010 — not my lucky day, obviously)]:

(...)

I have been trying to reproduce A108668 in the OEIS:

http://www.research.att.com/~njas/sequences/A108668

However, when I try to run the sequence as described I get:

0, 15, 35, 49, 51, 59, 90, 96, 210, 212, 242, 246, 248, 252, 283, 288, 297, ...

which differs by not including 71, 81, 84.

My string starts like this:

0(1)234(5)67(8)91(0)1(1)1(2)(1)3(1)(4)15(1)(6)(1)718(1)9(2)0(2)1(2)2(2)32(4)(2)5(2)6(2)(7)282(9)(3)0(3)(1)(3)233

(3)(4)35(3)6(3)7(3)839(4)0(4)(1)(4)2(4)34(4)(4)54(6)(4)74(8)49(5)(0)51(5)2(5)(3)(5)45(5)(5)6(5)75(8)59(6)0(6)(1)6

(2)(6)3(6)465(6)6(6)(7)6(8)697(0)(7)17(2)(7)(3)7(4)757(6)(7)778(7)9(8)(0)(8)18(2)(8)3(8)4(8)58(6)(8)7(8)8(8)(9)90

(9)(1)929(3)(9)4(9)(5)96(9)79(8)(9)910(0)

This would indicate that 71, 81, and 84 should not be in the sequence. However, I'm not 100% certain I have followed the description as intended.

The sequence is obviously finite because it is clearly impossible to have more than 10 digits in a row without erasure. Hence, the largest member is certainly less than 10^10.

[Éric A.]:

You are absolutely right, Sean — no room for 71, our sequence is wrong from 59 on...

Could you —or someone else— send me 100 terms (and correct the database accordingly)?

Many thanks (and apologizes).

Sean was quick to answer:

S = 0, 15, 35, 49, 51, 59, 90, 96, 210, 212, 242, 246, 248, 252, 283, 288, 297, 313, 315, 317, 319, 326, 349, 359, 392, 413, 420, 432, 486, 579, 581, 612, 615, 632, 688, 692, 759, 768, 779, 786, 812, 820, 842, 847, 854, 872, 880, 886, 910, 959, 991, 3210, 3212, 3310, 3312, 3422, 3938, 3980, 3988, 3991, 4373, 4485, 4565, 4716, 4718, 4720, 5254, 5275, 5393, 5430, 5434, 5929, 5946, 6210, 6212, 6237, 6258, 6286, 6412, 6426, 6430, 6434, 6545, 6650, 6750, 6916, 6989, 7210, 7217, 7262, 7344, 7353, 7368, 7616, 7664, 8216, 8341, 8445, 8494, 8613, 8652, 8740, 8750, 8816, 8820, 9252, 9291, 9497, 9632, 9657, 9750, 9755, 9823, 9833, 9843, 9890, 9930, 43717, 43993, 44210, 44212, 44222, 44252, 44512, 44612, 44713, 45281, 45893, 45953, 46248, 46278, 46288, 46412, 46422, 46522, 46622, 46844, 47317, 47381, 48212, 48232, 48268, 48312, 48322, 48480, 48488, 48514, 48520, 48726, 48810, 49223, 49279, 49413, 49531, 49860, 53221,...

Ray Chandler, August 17^th:

> I have calculated terms up to 10^8 with the latest being a(3486)=99998643.

Sean, August 17^th::

> I concur, a(3486)=99998643.

Sean, August 18^th:

> I think, a(4890)=9999854622 is the last term.

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