A344865 a(n) is the largest k such that no subsequence of n numbers appears more than once in the sequence of the first k prime gaps while overlapping subsequences are allowed.

2, 5, 6, 7, 19, 59, 88, 89, 1213, 1214, 3876, 3877, 3878, 10252040

Offset

1,1

Links

Table of n, a(n) for n=1..14.

Example

a(5) is 19 because when we look at the first 19 prime gaps, there is no sequence of 5 numbers that occurs twice. If we look at the first 20 prime gaps, there is a repetition.

Prog

(Python)
from sympy import primerange
list_of_prime_gaps = [x - y for x, y in zip(primerange(3, 40000),
primerange(1, 40000))]
def a(n):
    saved = set()
    for i in range(1, len(list_of_prime_gaps)-n):
        sequence = list_of_prime_gaps[i:i+n]
        if tuple(sequence) in saved:
            return i + n - 1
        saved.add(tuple(sequence))
    return None
for n in range(1, 14):
    print(a(n), end=", ")

Crossrefs

Cf. A001223 (prime gaps).

Sequence in context: A014489 A286270 A346880 * A350130 A033959 A167455

Adjacent sequences: A344862 A344863 A344864 * A344866 A344867 A344868

Keyword

nonn,more

Author

Armin Schäfer, May 31 2021

Extensions

a(14) from Armin Schäfer, Aug 08 2021

Status

approved