A362746 a(1)=a(2)=1; a(n)=The count of all occurrences in the list so far where integer a(n-1) appears adjacent to integer a(n-2).

1, 1, 2, 1, 2, 2, 2, 3, 1, 1, 4, 1, 2, 3, 2, 3, 3, 2, 4, 1, 3, 2, 5, 1, 1, 6, 1, 2, 4, 2, 3, 6, 1, 3, 3, 4, 1, 4, 4, 2, 4, 4, 4, 5, 1, 2, 5, 2, 3, 7, 1, 1, 8, 1, 2, 6, 1, 4, 5, 2, 4, 5, 3, 1, 4, 6, 1, 5, 3, 2, 8, 1, 3, 5, 3, 4, 2, 6, 2, 3, 9, 1, 1, 10, 1, 2, 7

Offset

1,3

Links

Gavin Lupo, Table of n, a(n) for n = 1..10000

Gavin Lupo, Image of the first 100000 terms.

Example

a(1) = 1.
a(2) = 1.
a(3) = 2. How many 1's so far are adjacent to a 1? = 2.
a(4) = 1. How many 2's so far are adjacent to a 1? = 1.
a(5) = 2. How many 1's so far are adjacent to a 2? = 2.
a(6) = 2. How many 2's so far are adjacent to a 1? = 2.

Mathematica

K = {1, 1}; While[Length@K < 87, A = Position[K, Last@K]; c = 0; For[a = 1, a <= Length@A, a++, If[K[[A[[a]] - 1]] == {K[[Length@K - 1]]} || K[[A[[a]] + 1]] == {K[[Length@K - 1]]}, c++]]; AppendTo[K, c]]; Print[K] (* Samuel Harkness, May 08 2023 *)

Prog

(Python)
from itertools import islice
from collections import Counter
def agen(): # generator of terms
    aprev, an, anext, c = 0, 1, 1, Counter({(1, 1)})
    while True:
        aprev, an, anext = an, anext, c[an, anext]
        c[an, anext] += 1
        if aprev != anext: c[anext, an] +=  1
        yield an
print(list(islice(agen(), 100))) # Michael S. Branicky, May 02 2023

Crossrefs

Cf. A342585, A355271, A362890.

Sequence in context: A318662 A073610 A285797 * A131840 A179752 A085693

Adjacent sequences: A362743 A362744 A362745 * A362747 A362748 A362749

Keyword

nonn,easy,look

Author

Gavin Lupo, May 01 2023

Status

approved