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A218615 a(n) = binary code (shown here in decimal) of the position of natural number n in the beanstalk-tree A218776. 4
1, 3, 2, 6, 4, 14, 10, 26, 18, 58, 42, 122, 90, 106, 74, 202, 138, 458, 330, 970, 714, 842, 586, 1866, 1354, 1610, 1098, 3402, 2378, 3658, 2634, 6730, 4682, 14922, 10826, 31306, 23114, 27210, 19018, 59978, 43594, 51786, 35402, 109130, 76362, 117322, 84554, 248394 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The binary code is the same as used by function general-car-cdr of MIT/GNU Scheme: a zero bit represents a cdr operation (taking the right hand side branch in the binary tree), and a one bit represents a car (taking the left hand side branch in the binary tree). The bits are interpreted from LSB to MSB, and the most significant one bit, rather than being interpreted as an operation, signals the end of the binary code.
LINKS
MIT/GNU Scheme 9.1. documentation, Function general-car-cdr
FORMULA
a(1)=1, for odd n, a(n) = A004754(a(A011371(n))), for even n, a(n) = A004755(a(A011371(n))).
EXAMPLE
As we can traverse to 4 in A218776-tree (see the example there) by taking first the right branch (cdr) from the root, resulting bit 0 as the least significant bit of the code, then by taking the left branch (car) from 3 to get to 4, resulting bit 1 as the second rightmost bit of the code, which when capped with an extra termination-one, results binary code 110, 6 in decimal, thus a(4)=6.
PROG
(Scheme with memoization macro definec): (definec (A218615 n) (cond ((< n 2) n) ((odd? n) (A004754 (A218615 (A011371 n)))) (else (A004755 (A218615 (A011371 n))))))
CROSSREFS
a(n) = A054429(A218614(n)). Superset of A218791. Used to construct A218776, A218777. Cf. also A179016, A218787, A218788
Sequence in context: A164073 A286595 A348404 * A177828 A248479 A304533
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Nov 16 2012
STATUS
approved

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Last modified July 14 22:45 EDT 2024. Contains 374323 sequences. (Running on oeis4.)