A262896 If n is in A262892, a(n) = A259934(n), otherwise the largest term in A045765 from which A259934(n) can be reached by iterating A049820, without visiting any other (larger) term of A259934.

8, 2, 79, 12, 18, 40, 30, 140, 42, 52, 54, 66, 68, 123, 98, 90, 94, 116, 106, 126, 164, 121, 369, 133, 156, 168, 180, 184, 280, 229, 190, 194, 210, 218, 252, 246, 236, 242, 272, 254, 312, 324, 300, 364, 298, 302, 372, 356, 334, 342, 346, 354, 439, 366, 374, 390, 672, 414, 410, 438, 426, 460, 442, 452, 470, 466, 564, 496, 494, 524, 627, 530, 546, 558, 562, 566, 574, 592, 859, 660, 606, 642, 708, 650

Offset

0,1

Comments

a(n) is the largest leaf-node among the finite subtrees branching from node n in the infinite trunk (A259934) of the tree generated by edge-relation A049820(child) = parent, and A259934(n) itself if it is one of the nonbranching nodes (A262897).

Note that without (so far undetected) regularity in A262509, there is no a priori upper bound for the value of a(n), and for some n this might not even be finite, if it happens that contrary to its conjectured nature, A259934 is not the unique infinite component, but just the lexicographically earliest instance of multiple infinite branches of the tree. In that case we might consider this sequence to be well-defined only up to the least such node branching to multiple infinite components, or alternatively, we might mark the nonfinite values at those points with -1.

Links

Antti Karttunen, Table of n, a(n) for n = 0..10000

Max Alekseyev & Antti Karttunen, Standalone C++-program for computing this sequence

Formula

a(n) = max(A259934(n), Max_{k = A082284(A259934(n)) .. A262686(A259934(n))} [A049820(k) = A259934(n)] * A262522(k)).

(Here [ ] stands for Iverson bracket, giving as its result 1 only when A049820(k) = A259934(n), and 0 otherwise).

Other identities. For all n >= 0:

A262904(a(n)) = n. [A262904 works as a left inverse for this sequence.]

A259934(n) = A262679(a(n)).

For all n >= 1:

a(A262892(n)) = A259934(A262892(n)) = A262897(n).

Prog

(Scheme)
(define (A262896 n) (let ((t (A259934 n))) (let loop ((m t) (k (A262686 t))) (cond ((<= k t) m) ((= t (A049820 k)) (loop (max m (A262522 k)) (- k 1))) (else (loop m (- k 1)))))))

Crossrefs

Cf. A000005, A049820, A082284, A259934, A262509, A262522, A262679, A262686, A262890, A262892, A262897, A262904, A263081.

Sequence in context: A038280 A260039 A032761 * A188898 A176860 A281068

Adjacent sequences: A262893 A262894 A262895 * A262897 A262898 A262899

Keyword

nonn

Author

Antti Karttunen, Oct 06 2015

Status

approved