A108668 Self-erasure surviving integers in the concatenation of all nonnegative integers.

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

Offset

1,2

Comments

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".

String starts like this:

0(1)234(5)67(8)91(0)1(1)1(2)(1)3(1)(4)15(1)(6)...

^ <-- hit.............................^^ <-- hit

Conjecture: the sequence is finite. Last term?

Comments from Sean A. Irvine: (Start) 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)...

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)

Links

Sean A. Irvine, Table of n, a(n) for n = 1..4890 [The complete list of terms]

Eric Angelini and Alexandre Wajnberg, Self-erasing Champernownes decimal expansion

Eric Angelini and Alexandre Wajnberg, Self-erasing Champernownes decimal expansion (a) [Cached with permission]

Eric Angelini and Alexandre Wajnberg, Self-erasing Champernownes decimal expansion (b) [Cached with permission]

Crossrefs

Sequence in context: A143202 A321182 A268463 * A201018 A187400 A162280

Adjacent sequences: A108665 A108666 A108667 * A108669 A108670 A108671

Keyword

base,easy,fini,full,nonn

Author

Eric Angelini and Alexandre Wajnberg, Jul 07 2005

Extensions

Corrected and extended by Sean A. Irvine, Aug 13 2010

Edited by Jon E. Schoenfield, Nov 29 2013

Status

approved