A390587 Primes generated by skipping a(n-1) - a(n-2) primes after a(n-1), starting with primes a(1)=2, a(2)=3.

2, 3, 7, 23, 101, 571, 4211, 40151, 481939, 7083227, 124498109, 2566114333, 61044579689, 1653951090889, 50474077479337, 1718590788936899, 64758818381898643, 2681499405853186489, 121260887431718186231

Offset

1,1

Comments

The difference a(n-1) - a(n-2) determines how many primes are skipped when selecting a(n).

Links

Table of n, a(n) for n=1..19.

Formula

a(n) = prime(primepi(a(n-1)) + a(n-1) - a(n-2) + 1) for n >= 3.

Example

a(3): d=3-2=1 -> skip 1 prime after 3 -> 7.
a(4): d=7-3=4 -> skip 4 primes after 7 -> 23.
a(5): d=23-7=16 -> skip 16 primes after 23 -> 101.

Mathematica

a[1] = 2; a[2] = 3; a[n_] := a[n] = Prime[PrimePi[a[n - 1]] + a[n - 1] - a[n - 2] + 1]; Array[a, 12] (* Amiram Eldar, Dec 11 2025 *)

Prog

(Python)
from sympy import prime, primepi
def a(n):
    if n < 3:
        return [2, 3][n-1]
    x, y = 2, 3
    for _ in range(3, n+1):
        x, y = y, prime(primepi(y) + y - x + 1)
    return y
(PARI)
a(n)={
  if(n==1, return(2));
  if(n==2, return(3));
  my(i=2, p=3, q=2);
  for(k=3, n,
       i+=p-q+1;
       q=p;
       p=prime(i)
  );
  p
}

Crossrefs

Cf. A000040, A006450, A007097, A036234, A102540, A119533.

Sequence in context: A087164 A077213 A387205 * A112601 A181609 A205827

Adjacent sequences: A390584 A390585 A390586 * A390588 A390589 A390590

Keyword

nonn,hard,more

Author

Gilligan Brobert, Dec 11 2025

Extensions

a(13)-a(19) from Amiram Eldar, Dec 11 2025

Status

approved