A187180 -id:A187180 - cp's OEIS frontend

A187186 Parse the infinite string 0123456701234567012345670... into distinct phrases 0, 1, 2, 3, 4, 5, 6, 7, 01, 23, 45, 67, 012, 34, ...; a(n) = length of n-th phrase.

1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 5, 4, 4, 5, 4, 4, 5, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 10, 10, 10, 10, 11, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 12, 12, 13, 12, 12, 13, 12, 12, 13, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 15, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15

Offset: 1

N. J. A. Sloane, Mar 06 2011

nonn

See A187180 for details.

Ray Chandler, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

See A187180-A187188 for alphabets of size 2 through 10.

After the initial block of eight 1's, the sequence is quasi-periodic with period 64, increasing by 8 after each block.

A187201 Parse Gijswijt's sequence A090822 into distinct phrases 1, 12, 11, 2, 22, 3, 112, 1122, 23, ...; a(n) = length of n-th phrase.

Original entry on oeis.org

1, 2, 2, 1, 2, 1, 3, 4, 2, 2, 3, 3, 3, 4, 3, 2, 3, 4, 3, 5, 4, 6, 3, 4, 4, 2, 7, 3, 4, 3, 5, 5, 5, 8, 3, 4, 5, 5, 5, 4, 2, 5, 5, 6, 4, 7, 4, 6, 5, 5, 6, 6, 6, 5, 4, 2, 8, 3, 7, 6, 6, 8, 6, 3, 9, 10, 10, 9, 7, 7, 9, 10, 10, 9, 7, 7, 6, 5, 4, 8, 10, 8, 8, 4, 7, 6, 3, 8, 5, 6, 9, 4, 7, 8, 10, 11, 11, 8, 9, 4

Offset: 1

N. J. A. Sloane, Mar 06 2011

nonn

Index entries for sequences related to Gijswijt's sequence

Cf. A090822, A109337, A187180-A187880, A187199, A187200.

A288533 Parse A004736 into distinct phrases [1], [2], [1,3], [2,1], [4], [3], [2,1,5], [4,3], [2,1,6], ...; a(n) is the length of the n-th phrase.

Original entry on oeis.org

1, 1, 2, 2, 1, 1, 3, 2, 3, 1, 3, 2, 1, 2, 2, 2, 1, 2, 4, 1, 1, 2, 3, 3, 2, 3, 5, 1, 3, 3, 3, 1, 1, 2, 2, 4, 3, 2, 3, 4, 4, 1, 3, 4, 4, 2, 1, 2, 2, 5, 5, 1, 2, 4, 3, 5, 1, 1, 2, 3, 4, 5, 2, 2, 3, 5, 5, 3, 1, 3, 3, 3, 4, 5, 1, 2, 2, 4, 5, 6, 1, 2, 4, 4, 6, 4, 1, 2, 3, 4, 4, 6, 2, 1, 2, 3, 3, 5, 5, 4, 1, 2, 3, 5, 6, 6, 1, 1, 2, 3, 4, 5, 7, 3, 2, 3, 4, 4, 7, 6, 1, 3, 3, 4, 5, 6, 5, 1, 2, 2

Offset: 1

Lewis Chen, Jun 11 2017

nonn

The phrases are formed by the Ziv-Lempel encoding described in A106182. - Neal Gersh Tolunsky, Nov 30 2023

			Consider the infinite sequence [1,2,1,3,2,1,4,3,2,1,5,4,3,2,1,...], i.e., A004736. We can first take [1] since we've never used it before. Then [2]. For the third term, we've already used [1], so we must instead take [1,3].

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000

Cf. A109337, A106182, A187180, A187181, A187182, A187183, A187184, A187185, A187186, A187187, A187188, A187199, A187200.

# you should use program from internal format
a = set()
i = 2
s = "1"
seq = ""
while i < 100:
    j = i
    while j > 0:
        if s not in a:
            seq = seq + "," + str(len(s)-len(s.replace(",",""))+1)
            a.add(s)
            s = str(j)
        else:
            s = s + "," + str(j)
        j -= 1
    i += 1
print(seq[1:])

cp's OEIS Frontend

A187186 Parse the infinite string 0123456701234567012345670... into distinct phrases 0, 1, 2, 3, 4, 5, 6, 7, 01, 23, 45, 67, 012, 34, ...; a(n) = length of n-th phrase.

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A187201 Parse Gijswijt's sequence A090822 into distinct phrases 1, 12, 11, 2, 22, 3, 112, 1122, 23, ...; a(n) = length of n-th phrase.

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A288533 Parse A004736 into distinct phrases [1], [2], [1,3], [2,1], [4], [3], [2,1,5], [4,3], [2,1,6], ...; a(n) is the length of the n-th phrase.

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Python