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A303936 A fractal-like sequence: erasing all pairs of contiguous terms that do not sum up to a prime leaves the sequence unchanged. 6
1, 2, 3, 4, 5, 6, 8, 9, 7, 4, 13, 11, 12, 10, 19, 14, 5, 6, 17, 15, 8, 9, 20, 16, 7, 4, 13, 18, 21, 22, 23, 24, 25, 28, 26, 11, 12, 29, 27, 10, 19, 34, 30, 31, 32, 35, 33, 14, 5, 6, 17, 36, 38, 15, 8, 9, 20, 39, 37, 16, 7, 4, 13, 18, 41, 40, 21, 22, 45, 42, 47 (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 X > 3 not yet present inside another pair of parentheses;

  3) always end the content inside a pair of parentheses with the smallest integer Y > 3 not yet present inside another pair of parentheses such that X and Y have no digit in common;

  4) after a(1) = 1, a(2) = 2 and a(3) = 3, always try to extend the sequence with a duplicate of the oldest term of the sequence not yet duplicated; if this leads to a contradiction, open a new pair of parentheses.

LINKS

Lars Blomberg, Table of n, a(n) for n = 1..1000

EXAMPLE

Parentheses are added around each pair of terms that don’t sum up to a prime:

1, 2, 3, (4,5), (6,8), (9,7), 4, (13,11), (12,10), (19,14), 5, 6, (17,15), 8, 9, (20,16), 7, 4, 13,

Erasing all the parenthesized contents yields

1, 2, 3, (...), (...), (...), 4, (.....), (.....), (.....), 5, 6, (.....), 8, 9, (.....), 7, 4, 13,

We see that the remaining terms slowly rebuild the starting sequence.

CROSSREFS

Cf. A303845 for another “erasing criteria” (prime by concatenation), A303948 (pair sharing a digit), A274329 (pair summing up to a prime), A302389 (pair having no digit in common).

Sequence in context: A318122 A265568 A265552 * A064364 A303645 A269855

Adjacent sequences:  A303933 A303934 A303935 * A303937 A303938 A303939

KEYWORD

nonn

AUTHOR

Eric Angelini, May 03 2018

STATUS

approved

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Last modified April 22 10:36 EDT 2019. Contains 322330 sequences. (Running on oeis4.)