A179757 -id:A179757 - cp's OEIS frontend

A179763 Binary expansions of A179757 concatenated together to a single binary sequence, so that from each term of A179757, the most significant bits come before the least significant bits.

1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0

Offset: 1

Antti Karttunen, Aug 03 2010

When viewed as a table, the first row contains six terms, the second eight, the third ten, and so on, i.e. row n contains 2(n+2) terms.

A. Karttunen, Table of n, a(n) for n = 1..593664 (containing 768 first rows)

Cf. also A179766 and A179758, A179761 & A179762. A179828-A179829.

A179830 The first central column of triangle A179757, i.e., A179763(1), A179763(8), A179763(17), A179763(28), ...

Original entry on oeis.org

1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0

Offset: 1

Antti Karttunen, Aug 03 2010

nonn

A. Karttunen, Table of n, a(n) for n = 1..1024

Cf. A179831-A179834, and also A179770, A179775.

a(n) = A179763(A028884(n+2)).

A122245 a(n) = A014486(A122244(n)).

Original entry on oeis.org

44, 232, 920, 3876, 14936, 60568, 248240, 996440, 3876264, 15524272, 63773584, 255477160, 993549616, 3970767760, 16350559552, 65386339632, 254129067336, 1016476056896, 4184726043136, 16740063237448, 65054466609736, 260416091191808

Offset: 1

Antti Karttunen, Sep 14 2006

Questions: to which Wolfram's class does this simple program belong, class 3 or class 4? (Is that classification applicable here? This is not 1D CA, although it may look like one).
Does the "central skyscraper" continue widening forever? (see the image for up to 16384th generation) At what specific points it widens? (A new sequence for that). How does that differ from A122242 and similar sister sequences, with different starting conditions?
Related comments in A179777.

Antti Karttunen, Table of n, a(n) for n = 1..1024
A. Karttunen, Python program for computing this sequence and the associated image.
A. Karttunen, Terms a(1)-a(768) drawn as binary strings, in Wolframesque fashion.
A. Karttunen, Terms a(1)-a(256) drawn as binary strings, showing details better.
Antti Karttunen, The central parts of terms a(1) - a(16384) drawn in similar fashion, showing how the "crystallized central skyscraper" gets slowly wider and wider

A122246 shows the same sequence in binary. Compare to similar Wolframesque plots given in A080070, A122229, A122232, A122235, A122239, A122242, A179755, A179757. Cf. also A179777, A179762, A179417.

A179832 Position of ones in A179831.

Original entry on oeis.org

5, 8, 9, 13, 15, 16, 20, 21, 25, 29, 33, 40, 41, 48, 49, 55, 56, 61, 72, 79, 82, 83, 84, 90, 92, 93, 101, 102, 106, 109, 113, 116, 117, 118, 122, 123, 126, 133, 134, 140, 141, 142, 143, 150, 155, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177

Offset: 1

Antti Karttunen, Aug 03 2010

nonn

Look at the central column of A179757. Conjecture, from a(46)=165 onward, all integers >= 165 present.

A. Karttunen, Table of n, a(n) for n = 1..150
A. Karttunen, Terms a(1)-a(700) of A179757 drawn as binary strings, 3x3 pixels per bit.

Cf. A179833-A179834, and also A179772, A179777.

A179756 Iterates of A122237 starting from the initial value 8.

Original entry on oeis.org

8, 20, 57, 167, 569, 1832, 5693, 19241, 72004, 251434, 817685, 2912603, 11464927, 41520649, 137255398, 502535651, 2038965137, 7539964485, 25351037019, 94403539934, 389919393256, 1461664899103, 4982806264910, 18769209002168

Offset: 1

Antti Karttunen, Aug 03 2010

nonn

See the illustrations at A179757.

Antti Karttunen, Table of n, a(n) for n = 1..1024

Cf. A122237, A179757.

(define (A179756 n) (if (= 1 n) 8 (A122237 (A179756 (-1+ n)))))

a(1) = 8, a(n) = A122237(A179756(a(n-1))).

A179755 a(n) = A014486(A179754(n)).

Original entry on oeis.org

50, 216, 868, 3492, 13976, 56472, 225880, 897624, 3590576, 14471600, 57886120, 229868968, 919477136, 3706264464, 14825053488, 58832739632, 235330977088, 948740144448, 3794960504136, 15061020431688, 60244082031104

Offset: 1

Antti Karttunen, Aug 03 2010

nonn

A. Karttunen, Table of n, a(n) for n = 1..1024
A. Karttunen, Python program for computing this sequence and the associated images.
A. Karttunen, Terms a(1)-a(768) drawn as binary strings, one pixel per bit.
A. Karttunen, Terms a(1)-a(700) drawn as binary strings, 3x3 pixels per bit.

a(n+1) = A004758(A179757(n)). Cf. also A122242, A122245.

cp's OEIS Frontend

A179763 Binary expansions of A179757 concatenated together to a single binary sequence, so that from each term of A179757, the most significant bits come before the least significant bits.

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A179830 The first central column of triangle A179757, i.e., A179763(1), A179763(8), A179763(17), A179763(28), ...

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A122245 a(n) = A014486(A122244(n)).

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A179832 Position of ones in A179831.

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A179756 Iterates of A122237 starting from the initial value 8.

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A179755 a(n) = A014486(A179754(n)).

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