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

1,4

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)

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

Prog

(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))));

Crossrefs

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

Cf. also A374214, A374482, A374483.

Sequence in context: A110898 A264756 A267942 * A147994 A106365 A200174

Adjacent sequences: A374478 A374479 A374480 * A374482 A374483 A374485

Keyword

nonn

Author

Antti Karttunen, Jul 09 2024

Status

approved