A374481 The distance from prime(n) to the nearest common ancestor of prime(n) and 1+prime(n) in the Doudna-tree (A005940).

0, 1, 1, 3, 3, 2, 6, 5, 7, 8, 10, 4, 10, 9, 13, 15, 15, 7, 12, 19, 9, 19, 20, 22, 24, 20, 21, 27, 26, 23, 30, 28, 25, 32, 34, 28, 15, 25, 36, 31, 39, 39, 41, 19, 41, 45, 31, 44, 42, 43, 46, 50, 52, 51, 42, 52, 55, 51, 25, 46, 41, 61, 61, 59, 28, 51, 44, 67, 60, 68, 55, 70, 64, 71, 69, 74, 73, 32, 61, 69, 79, 35, 82

Offset: 1

Author

Antti Karttunen, Jul 09 2024

Keywords

• nonn

Comments

Question: Is there any reasonable lower bound for this sequence?

Considering k that do not occur as terms of this sequence, see also A374214.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000040, A000203, A005940, A059305, A241917, A252464, A319988, A348040, A347381.

Cf. also A374214, A374482, A374483.

Programs

PARI

A374481(n) = A347381(prime(n));

PARI

A241917(n) = if(isprime(n), primepi(n), if(1>=omega(n), 0, my(f=factor(n)); if(f[#f~,2]>1, 0, primepi(f[#f~,1])-primepi(f[(#f~)-1,1]))));
A374481(n) = if(1==n,0,(-1+n-A241917(1+prime(n))));

Formula

a(n) = A347381(A000040(n)) = n - A348040(A000040(n), 1+A000040(n)).

For all n >= 1, a(A059305(n)) = A059305(n)-1.

If A319988(1+A000040(n)) then a(n) = n-1.

For n > 1, a(n) = n - A241917(1+prime(n)) - 1. - Peter Munn and Antti Karttunen, Jul 10 2024