The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A303948 A fractal-like sequence: erasing all pairs of consecutive terms that have at least one digit in common leaves the sequence unchanged. 10
 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 12, 30, 13, 22, 21, 33, 23, 10, 24, 14, 25, 15, 26, 16, 27, 17, 28, 18, 29, 19, 32, 31, 40, 34, 11, 20, 35, 36, 12, 30, 41, 42, 13, 22, 37, 38, 21, 33, 44, 43, 50, 45, 23, 10, 24, 39, 49, 51, 52, 14, 25, 46, 47, 15, 26, 48, 54, 16, 27, 53, 55, 17, 28 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The sequence is fractal-like as it embeds an infinite number of copies of itself. The sequence was built according to these rules (see, in the Example section, the parenthesization technique):   1) no overlapping pairs of parentheses;   2) always start the content inside a pair of parentheses with the smallest integer S > 9 not yet present inside another pair of parentheses;   3) always end the content inside a pair of parentheses with the smallest integer H > 9 not yet present inside another pair of parentheses such that the integers S and H have at least one digit in common;   4) after a(1) = 1, a(2) = 2, a(3) = 3, a(4) = 4, a(5) = 5, a(6) = 6, a(7) = 7, a(8) = 8, a(9) = 9, a(10) = 10, always try to extend the sequence with a duplicate > 9 of the oldest term of the sequence not yet duplicated; if this leads to a contradiction, open a new pair of parentheses;   5) Never use a term of A171102 (Pandigital numbers: numbers containing the digits 0-9. Version 2: each digit appears at least once). LINKS Lars Blomberg, Table of n, a(n) for n = 1..10000 EXAMPLE Parentheses are added around each pair of terms having at least one digit in common: 1,2,3,4,5,6,7,8,9,(10,11),(20,12),(30,13),(22,21),(33,23),10,(24,14),(25,15),(26,16),(27,17),(28,18),(29,19),(32,31),(40,34),11,20,(35,36),12,30,(41,42),13, Erasing all the parenthesized contents yields 1,2,3,4,5,6,7,8,9,(.....),(.....),(.....),(.....),(.....),10,(.....),(.....),(.....),(.....),(.....),(.....),(.....),(.....),11,20,(.....),12,30,(.....),13, We see that the remaining terms slowly rebuild the starting sequence. CROSSREFS Cf. A303845 for another "erasing criterion" (prime by concatenation). Sequence in context: A239217 A130571 A275512 * A275413 A273376 A247758 Adjacent sequences:  A303945 A303946 A303947 * A303949 A303950 A303951 KEYWORD nonn,base AUTHOR Eric Angelini and Lars Blomberg, May 03 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 29 07:08 EDT 2020. Contains 337425 sequences. (Running on oeis4.)