

A255066


The trunk of numberofruns beanstalk (A255056) with reversed subsections.


8



0, 2, 6, 4, 14, 12, 10, 30, 28, 26, 22, 18, 62, 60, 58, 54, 50, 46, 42, 36, 32, 126, 124, 122, 118, 114, 110, 106, 100, 96, 94, 90, 84, 78, 74, 68, 64, 254, 252, 250, 246, 242, 238, 234, 228, 224, 222, 218, 212, 206, 202, 196, 192, 190, 186, 180, 174, 168, 162, 156, 152, 148, 142, 138, 132, 128, 510
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OFFSET

0,2


COMMENTS

This can be viewed as an irregular table: after the initial zero on row 0, start each row n with term x = (2^(n+1))2 and subtract repeatedly the number of runs in binary representation of x to get successive x's, until the number that has already been listed (which is always (2^n)2) is encountered, which is not listed second time, but instead, the current row is finished [and thus containing only terms of equal binary length, A000523(n) on row n]. The next row then starts with (2^(n+2))2, with the same process repeated.


LINKS

Antti Karttunen, Table of n, a(n) for n = 0..16142; Rows 0..16, flattened


FORMULA

a(0) = 0, a(1) = 2, a(2) = 6; and for n > 2, a(n) = A004755(A004755(A236840(a(n1)))) if A236840(a(n1))+2 is power of 2, otherwise just A236840(a(n1)) [where A004755(x) adds one 1bit to the left of the most significant bit of x].
In other words, for n > 2, let k = A236840(a(n1)). Then, if k+2 is not a power of 2, a(n) = k, otherwise a(n) = k + (6 * (2^A000523(k))).
Other identities. For all n >= 0:
a(n) = A255056(A255122(n)).


EXAMPLE

Rows 0  5 of the array:
0;
2;
6, 4;
14, 12, 10;
30, 28, 26, 22, 18;
62, 60, 58, 54, 50, 46, 42, 36, 32;
After row 0, the length of row n is given by A255071(n).


PROG

(Scheme, with memoizationmacro definec)
(definec (A255066 n) (cond ((< n 2) (+ n n)) ((= n 2) 6) ((A236840 (A255066 ( n 1))) => (lambda (next) (if (pow2? (+ 2 next)) (A004755 (A004755 next)) next)))))
(define (pow2? n) (and (> n 0) (zero? (A004198bi n ( n 1))))) ;; A004198bi implements bitwise and. See A004198, A209229.


CROSSREFS

Cf. A255067 (same seq, terms divided by 2).
Cf. A255071 (gives row lengths).
Cf. A000523, A004755, A005811, A236840, A255056, A255122.
Analogous sequences: A218616, A230416.
Sequence in context: A286712 A268716 A204985 * A184364 A226569 A111807
Adjacent sequences: A255063 A255064 A255065 * A255067 A255068 A255069


KEYWORD

nonn,base,tabf


AUTHOR

Antti Karttunen, Feb 14 2015


STATUS

approved



