A379444 a(n) is the difference between the least prime > (n+1)^2 and the largest prime < n^2, divided by 2.

4, 5, 8, 7, 11, 10, 11, 11, 15, 18, 17, 15, 17, 17, 21, 24, 25, 21, 23, 24, 31, 27, 30, 29, 30, 30, 40, 34, 40, 39, 35, 38, 38, 37, 41, 40, 42, 45, 48, 54, 51, 51, 47, 56, 50, 51, 57, 52, 66, 57, 60, 57, 64, 57, 65, 71, 65, 69, 67, 64, 78, 66, 68, 69, 72, 77, 81

Offset

2,1

Comments

2*a(n) would be the gap needed between consecutive primes to provide a counterexample to Legendre's conjecture that there is always a prime between n^2 and (n+1)^2. The gaps actually observed are significantly smaller; see A378904 for comparison.

Links

Hugo Pfoertner, Table of n, a(n) for n = 2..10000

Formula

a(n) = (A007491(n+1) - A053001(n))/2.

a(n) >= n + 2.

Prog

(PARI) a379444(n) = (nextprime((n+1)^2) - precprime(n^2))/2

Crossrefs

Cf. A001223, A007491, A053001, A058043, A350100, A378904.

Sequence in context: A021222 A132023 A378909 * A107758 A104883 A154885

Adjacent sequences: A379427 A379428 A379429 * A379448 A379451 A379452

Keyword

nonn,easy,new

Author

Hugo Pfoertner, Dec 23 2024

Status

approved