The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A303536 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A303536

Number of terms in greedy partition of n into binary palindromes.
(history; published version)

#27 by Bruno Berselli at Mon May 14 07:45:40 EDT 2018

STATUS

reviewed

approved

#26 by Michel Marcus at Mon May 14 07:08:29 EDT 2018

STATUS

proposed

reviewed

#25 by Altug Alkan at Sun May 13 05:55:53 EDT 2018

STATUS

editing

proposed

#24 by Altug Alkan at Sun May 13 05:50:59 EDT 2018

COMMENTS

The position where n = 0.. occurs for the first time: 0, 1, 2, 11, 44, 557, 131630, ... - Antti Karttunen, and _Altug Alkan_, May 13 2018

STATUS

proposed

editing

Discussion

Sun May 13

05:55

Altug Alkan: Thanks for the comment, in here I believe that there is a pattern like that
(2^(2*(#binary(2))-1)+1 + 2^(2*(#binary(1))-1)+1 -4 )/4  = 2,
(2^(2*(#binary(4))-1) +1+ 2^(2*(#binary(2))-1)+1 +  2^(2*(#binary(1))-1)+1 -1 )/4 = 11, (2^(2*(#binary(11))-1)+1 + 2^(2*(#binary(4))-1) +1+ 2^(2*(#binary(2))-1)+1+  2^(2*(#binary(1))-1)+1 +2 )/4  = 44, (2^(2*(#binary(44))-1)+1+2^(2*(#binary(11))-1)+1 + 2^(2*(#binary(4))-1) +1+ 2^(2*(#binary(2))-1)+1+  2^(2*(#binary(1))-1)+1 +5 )/4  = 557, (2^(2*(#binary(557))-1)+1+2^(2*(#binary(44))-1)+1+2^(2*(#binary(11))-1)+1 + 2^(2*(#binary(4))-1) +1+ 2^(2*(#binary(2))-1)+1+  2^(2*(#binary(1))-1)+1 +8 )/4  =131630,... Each term determines the other with this way. I will prove it when I have time to do this. It based on simple idea in root. Best regards.

#23 by Antti Karttunen at Sun May 13 03:27:58 EDT 2018

STATUS

editing

proposed

#22 by Antti Karttunen at Sun May 13 03:25:54 EDT 2018

LINKS

<a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

Discussion

Sun May 13

03:27

Antti Karttunen: Altug: If you know more terms for my new "records" comment: "The position where n = 0.. occurs for the first time: ..." then please add them (appending also your name after mine then to the attribution). I guess 131630 is the next one after 557, based on your example.

#21 by Antti Karttunen at Sun May 13 03:25:00 EDT 2018

COMMENTS

The position where n = 0.. occurs for the first time: 0, 1, 2, 11, 44, 557, - Antti Karttunen, May 13 2018

LINKS

Antti Karttunen, <a href="/A303536/b303536.txt">Table of n, a(n) for n = 0..65537</a>

#20 by Antti Karttunen at Sun May 13 03:14:16 EDT 2018

FORMULA

a(0) = 0; for n > 0, a(n) = 1 + a(A303534(n)). [We are iterating the map n -> A303534(n) until zero is reached.] - Antti Karttunen, May 13 201, 2018, after the an earlier comment: We are iterating the process n -> A303534(n).

#19 by Antti Karttunen at Sun May 13 03:10:42 EDT 2018

FORMULA

a(0) = 0; for n > 0, a(n) = 1 + a(A303534(n)). - Antti Karttunen, May 13 2018201, after the comment: We are iterating the process n -> A303534(n).

CROSSREFS

We are iterating the process n -> A303534(n).

Cf. A006995 gives the (binary palindromes), A206913, A259656, A303534.

Cf. A006995, A206913, A303534.

#18 by Antti Karttunen at Sun May 13 03:08:12 EDT 2018

FORMULA

a(0) = 0; for n > 0, a(n) = 1 + a(A303534(n)). - Antti Karttunen, May 13 2018

PROG

(PARI)

isA006995(n) = Vecrev(n=binary(n))==n;

A303534(n) = {my(k=0); while(!isA006995(n-k), k++); k; } \\ From A303534

A303536(n) = if(!n, n, 1+A303536(A303534(n))); \\ Antti Karttunen, May 13 2018

CROSSREFS

Cf. A006995, A206913, A303534.

STATUS

proposed

editing