A249900 Sequence which reappears when consecutive terms are erased iff they both are either prime or nonprime.

1, 2, 3, 4, 6, 2, 8, 9, 3, 4, 5, 7, 6, 2, 8, 11, 13, 9, 3, 4, 5, 10, 12, 7, 6, 2, 8, 11, 14, 15, 13, 9, 3, 4, 5, 10, 17, 19, 12, 7, 6, 2, 8, 11, 14, 23, 29, 15, 13, 9, 3, 4, 5, 10, 17, 16, 18, 19, 12, 7, 6, 2, 8, 11, 14, 23, 20, 21, 29, 15, 13, 9, 3, 4, 5

Offset

0,2

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Éric Angelini, More fractal triangles (with primes), SeqFan list, Jan 12 2015.

Example

.   n : 0|1|2|3|4|5|6|7|8|9|10|11|12|13|14|15|16|17|18|19|20|21|22|23|24|
. a(n): 1 2 3 4 6 2 8 9 3 4  5  7  6  2  8 11 13  9  3  4  5 10 12  7  6
. p/c : - p p c c p c c p c  p  p  c  p  c  p  p  c  p  c  p  c  c  p  c
.     : 1 _ _ _ _ 2 _ _ 3 4  _  _  6  2  8  _  _  9  3  4  5  _  _  7  6  .

Prog

(Haskell)
a249900 n = a249900_list !! n
a249900_list = [1..4] ++ concatMap (uncurry (++))
          (f [2] [3, 4] (drop 2 a000040_list) (tail a002808_list)) where
   f us@(u:_) vs ps'@(p:p':ps) cs'@(c:c':cs)
     | a010051 u == 1 = g ([c] ++ us ++ [c']) vs ps' cs
     | otherwise      = g ([p] ++ us ++ [p']) vs ps cs'
   g us vs@(v:_) (p:ps) (c:cs) = (us, ws) : f us ws ps cs where
     ws = if a010051 v == 1 then [c] ++ vs ++ [p] else [p] ++ vs ++ [c]

Crossrefs

Cf. A010051, A000040, A002808; A249484.

Sequence in context: A030378 A280244 A203138 * A260272 A321479 A128332

Adjacent sequences: A249897 A249898 A249899 * A249901 A249902 A249903

Keyword

nonn

Author

Eric Angelini and Reinhard Zumkeller, Jan 13 2015

Status

approved