A344582 a(n) is the least k such that there are exactly n primes between prime(k) + 1 and floor(prime(k + 1)^2/prime(k)) (inclusive) or 0 if no such k exists.

1, 2, 4, 30, 180, 462, 890, 1532, 3385, 19871, 29040, 59257, 66762, 31545, 597311, 1448751, 1421021, 1293698, 12768473, 2279181, 147165284, 118374763, 821495413, 2618883054, 2247521689, 3145845927, 7650216016, 27357920380, 22859974504, 189924891289, 78076882908, 189573830057

Offset

1,2

Comments

a(n) is the least k such that A228098(k) = n.

Links

Table of n, a(n) for n=1..32.

Example

a(4) = 30 as there are exactly 4 primes between prime(30) + 1 = 114 and floor(prime(31)^2/prime(30)) = 142 namely the four primes 127, 131, 137 and 139.

Prog

(PARI) upto(n) = {my(i, p, q, res = vector(1)); i = 1; p = 2; forprime(q = 3, oo, u = q^2\p; t = 1; forprime(r = q + 1, u, t++); if(t > #res, res = concat(res, vector(t - #res))); if(res[t] == 0, res[t] = i; ); p = q; i++; if(i > n, return(res))); }

Crossrefs

Cf. A228098, A230777.

Sequence in context: A058779 A359914 A230777 * A241542 A241540 A349265

Adjacent sequences: A344579 A344580 A344581 * A344583 A344584 A344585

Keyword

nonn

Author

David A. Corneth, May 24 2021

Extensions

a(24)-a(32) from Martin Ehrenstein, Jun 02 2021

Status

approved