A369858 Number of fixed elements when the first n prime gaps are sorted.

0, 1, 2, 3, 4, 3, 4, 5, 6, 7, 5, 6, 6, 6, 7, 8, 9, 8, 9, 10, 9, 10, 9, 10, 11, 10, 10, 11, 11, 10, 11, 11, 11, 9, 9, 12, 11, 11, 12, 13, 14, 13, 13, 16, 17, 17, 17, 18, 19, 20, 18, 18, 18, 18, 18, 18, 19, 18, 19, 18, 18, 18, 19, 19, 20, 21, 22, 22, 22, 20, 20, 19, 19, 20, 20, 20

Offset

0,3

Comments

Let G = A001223(1..n) be the first n prime gaps, and H = sort(G) the sequence of the same terms but in nondecreasing order. Then a(n) counts the zeros in G-H.

StackExchange user Daniel Tisdale described this sequence in 2014 and observed that the sequence appeared to grow like primepi(n) ~ n/log(n). It is not presently known if that is true.

Links

Table of n, a(n) for n=0..75.

Daniel Tisdale, Sorting of prime gaps, math.StackExchange.com, Aug. 11, 2014.

Prog

(PARI) apply( {A369858(n, p=primes(n+1))=#[0|d<-vecsort(p=p[^1]-p[^-1])-p, !d]}, [0..99]) \\ M. F. Hasler, Apr 24 2024
(Python)
from sympy import prime
A1223=[] # this list starts at index 0, unlike function A001223
def A369858(n):
    if (L:= len(A1223)) < n:
        A1223.extend(prime(k+2)-prime(k+1) for k in range(L, n))
    return sum(a==b for a, b in zip(A1223[:n], sorted(A1223[:n]))) # M. F. Hasler, Apr 26 2024

Crossrefs

Cf. A001223 (prime gaps).

Sequence in context: A280242 A325953 A245343 * A341019 A360535 A255938

Adjacent sequences: A369855 A369856 A369857 * A369859 A369860 A369861

Keyword

nonn

Author

M. F. Hasler, Apr 24 2024

Status

approved