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%I #18 Jun 15 2021 11:03:20
%S 0,15,35,49,51,59,90,96,210,212,242,246,248,252,283,288,297,313,315,
%T 317,319,326,349,359,392,413,420,432,486,579,581,612,615,632,688,692,
%U 759,768,779,786,812,820,842,847,854,872,880,886,910,959,991,3210,3212,3310,3312
%N Self-erasure surviving integers in the concatenation of all nonnegative integers.
%C Concatenation of the nonnegative integers is: 012345678910111213141516... Read the leftmost digit [0], jump accordingly *over* 0 digits and erase the one you're landing on (here, 1): you get 0(1)2345678910111213141516... (erased digits are put between parentheses). Read now the leftmost unread and visible digit [2], jump accordingly *over* 2 (visible) digits and erase the one you're landing on (5): you get 0(1)234(5)678910111213141516... Read again the leftmost unread digit [3], jump accordingly *over* 3 digits and erase the one you're landing on (8): you get 0(1)234(5)67(8)910111213141516..., etc. At the end of the (infinite) procedure, keep the integers which appear to be at the same place as in the starting concatenation but which stand also between two erased digits [something like: ...(a)15(b)...]. "0" and 15 are the first such "survivors".
%C String starts like this:
%C 0(1)234(5)67(8)91(0)1(1)1(2)(1)3(1)(4)15(1)(6)...
%C ^ <-- hit.............................^^ <-- hit
%C Conjecture: the sequence is finite. Last term?
%C Comments from _Sean A. Irvine_: (Start) My string starts like this:
%C 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)\
%C 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)\
%C 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\
%C (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)\
%C 58(6)(8)7(8)8(8)(9)90(9)(1)929(3)(9)4(9)(5)96(9)79(8)(9)910(0)...
%C 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. In fact a(4890)=9999854622 is the last term. (End)
%H Sean A. Irvine, <a href="/A108668/b108668.txt">Table of n, a(n) for n = 1..4890</a> [The complete list of terms]
%H Eric Angelini and Alexandre Wajnberg, <a href="http://www.cetteadressecomportecinquantesignes.com/SelfChampErase.htm">Self-erasing Champernownes decimal expansion</a>
%H Eric Angelini and Alexandre Wajnberg, <a href="/A108668/a108668.png">Self-erasing Champernownes decimal expansion (a)</a> [Cached with permission]
%H Eric Angelini and Alexandre Wajnberg, <a href="/A108668/a108668.pdf">Self-erasing Champernownes decimal expansion (b)</a> [Cached with permission]
%K base,easy,fini,full,nonn
%O 1,2
%A _Eric Angelini_ and _Alexandre Wajnberg_, Jul 07 2005
%E Corrected and extended by _Sean A. Irvine_, Aug 13 2010
%E Edited by _Jon E. Schoenfield_, Nov 29 2013
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