cp's OEIS Frontend

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

%I A374481 #26 Jul 10 2024 09:36:44
%S A374481 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,
%T A374481 27,26,23,30,28,25,32,34,28,15,25,36,31,39,39,41,19,41,45,31,44,42,43,
%U A374481 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
%N A374481 The distance from prime(n) to the nearest common ancestor of prime(n) and 1+prime(n) in the Doudna-tree (A005940).
%C A374481 Question: Is there any reasonable lower bound for this sequence?
%C A374481 Considering k that do not occur as terms of this sequence, see also A374214.
%H A374481 Antti Karttunen, <a href="/A374481/b374481.txt">Table of n, a(n) for n = 1..100000</a>
%H A374481 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A374481 a(n) = A347381(A000040(n)) = n - A348040(A000040(n), 1+A000040(n)).
%F A374481 For all n >= 1, a(A059305(n)) = A059305(n)-1.
%F A374481 If A319988(1+A000040(n)) then a(n) = n-1.
%F A374481 For n > 1, a(n) = n - A241917(1+prime(n)) - 1. - _Peter Munn_ and _Antti Karttunen_, Jul 10 2024
%o A374481 (PARI) A374481(n) = A347381(prime(n));
%o A374481 (PARI)
%o A374481 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]))));
%o A374481 A374481(n) = if(1==n,0,(-1+n-A241917(1+prime(n))));
%Y A374481 Cf. A000040, A000203, A005940, A059305, A241917, A252464, A319988, A348040, A347381.
%Y A374481 Cf. also A374214, A374482, A374483.
%K A374481 nonn
%O A374481 1,4
%A A374481 _Antti Karttunen_, Jul 09 2024