Alex Lauber - cp's OEIS frontend

User: Alex Lauber

Alex Lauber has authored 2 sequences.

A337064 a(n) is the index of the first occurrence of n in A337063, or -1 if n never appears.

0, 3, 5, 2, 16, 20, 30, 40, 9, 23, 90, 57, 110, 29, 36, 12, 220, 33, 342, 230, 163, 179, 494, 19, 15, 109, 128, 88, 694, 82, 744, 43, 125, 219, 169, 72, 1060, 373, 253, 85, 1205, 113, 1346, 151, 207, 564, 1726, 131, 75, 332

Offset: 1

Alex Lauber, Aug 13 2020

nonn

419 is the lowest number that does not appear in the first 100000 terms of A337063.

			A337063 starts {1, 1, 4, 2, ...} so a(2) = 3.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A337064

Cf. A337063, A316774 (adds the two previous terms), A316973 (similar index for the addition sequence).

PARI
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A337063 a(n) = 1 for n < 2; a(n) = freq(a(n-1),n) * freq(a(n-2),n) for n >= 2, where freq(i,j) is the number of times i appears in [a(0),a(1),...,a(j-1)].

Original entry on oeis.org

1, 1, 4, 2, 1, 3, 3, 4, 4, 9, 3, 3, 16, 4, 4, 25, 5, 1, 4, 24, 6, 1, 5, 10, 2, 2, 9, 6, 4, 14, 7, 1, 6, 18, 3, 5, 15, 3, 6, 24, 8, 2, 4, 32, 8, 2, 10, 10, 9, 9, 16, 8, 6, 15, 10, 8, 16, 12, 3, 7, 14, 4, 18, 18, 9, 15, 15, 16, 16, 25, 10, 10, 36, 6, 6, 49, 7, 3

Offset: 0

Alex Lauber, Aug 13 2020

nonn

Does this sequence contain every number?
Does each number appear only a finite number of times?
Starting with a(0)=0 and a(1)=1 gives the same sequence offset by one place.

			a(2) = occurrences of a(1)=1 in [a(0), a(1)]=[1, 1] * occurrences of a(0)=1 in [a(0), a(1)]=[1, 1] = 2*2 = 4.
a(3) = occurrences of a(2)=4 in [a(0), a(1), a(2)]=[1, 1, 4] * occurrences of a(1)=1 in [a(0), a(1), a(2)]=[1, 1, 4] = 1*2 = 2.

Rémy Sigrist, Table of n, a(n) for n = 0..25000
Rémy Sigrist, PARI program for A337063

Cf. A337064 (index of first occurrence of n).

Cf. A316774 (which adds the two previous terms), A316973.

PARI
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See Links section.
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More terms from Rémy Sigrist, Sep 18 2020

cp's OEIS Frontend

User: Alex Lauber

A337064 a(n) is the index of the first occurrence of n in A337063, or -1 if n never appears.

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