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
Keywords
Examples
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.
Programs
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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))); }
Extensions
a(24)-a(32) from Martin Ehrenstein, Jun 02 2021
Comments