A262522 a(n)=0 if n is in A259934, otherwise the largest term in A045765 from which one can reach n by iterating A049820 zero or more times.

0, 8, 0, 7, 8, 7, 0, 7, 8, 79, 20, 79, 0, 13, 20, 79, 24, 79, 0, 19, 20, 79, 0, 79, 24, 25, 40, 79, 28, 79, 0, 79, 40, 33, 0, 79, 36, 37, 140, 79, 40, 43, 0, 43, 50, 79, 0, 79, 140, 49, 50, 79, 52, 79, 0, 55, 56, 79, 0, 79, 140, 79, 0, 63, 64, 79, 66, 67, 68, 79, 0, 79, 140, 79, 74, 75, 123, 79, 0, 79, 88, 123, 98, 123, 140, 85, 98, 123, 88, 103, 0, 123, 98, 103, 0, 123

Offset: 0

Author

Antti Karttunen, Oct 04 2015

Keywords

• nonn

Comments

If n is itself in A045765, we iterate 0 times, and thus a(n) = n.

Examples

			For n=1, its transitive closure (as defined by edge-relation A049820(child) = parent) is the union of {1} itself together with all its descendants: {1, 3, 4, 5, 7, 8}. We see that there are no other nodes in a subtree whose root is 1, because A049820(3) = 3 - d(3) = 1, A049820(4) = 1, A049820(5) = 3, A049820(7) = 5, A049820(8) = 4 and of these only 7 and 8 are terms of A045765. The largest term (which by necessity is always a term of A045765) is here 8, thus a(1) = 8. Note however that it is not always the largest leaf from which starts the longest path leading back to n. (In this case it is 7 instead of 8, see the example in A262695).
For n=9, its transitive closure is {9, 11, 13, 15, 16, 17, 19, 21, 23, 24, 27, 29, 31, 33, 35, 36, 37, 39, 41, 43, 45, 47, 51, 53, 55, 57, 59, 61, 63, 64, 65, 67, 69, 71, 73, 75, 77, 79}. The largest term is 79, thus a(9) = 79.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..17724

Crossrefs

Cf. A000005, A045765, A049820, A060990, A082284, A259934, A262511, A262512, A262686, A262693.

Cf. A262679, A262695, A262696, A262697.

Formula

If A262693(n) = 1 [when n is in A259934],

then a(n) = 0,

otherwise, if A060990(n) = 0 [when n is one of the leaves, A045765],

then a(n) = n,

otherwise:

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

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

Other identities. For all n >= 1:

a(A262511(n)) = a(A262512(n)) = a(A082284(A262511(n))).