A082891 Smallest prime p[j] such that quotient q[j], obtained when consecutive prime differences are divided by logarithm of smaller prime,p[j], is larger than n.

2, 7, 1129, 1327, 19609, 31397, 155921, 370261, 1357201, 2010881, 20831323, 20831323

Offset

1,1

Comments

Is lim superior(q[n])=+infinity? See A082892.

Links

Table of n, a(n) for n=1..12.

Formula

a(n)=Min{p[x]; (p[x+1]-p[x])/log(p[x])>n}

Example

n=1319945: p[n+1]=20831533, p[n]=20831323, d=210, log[20831321]=16.852, q=210/16.852=12.4615>12 and first for >11 too.

Mathematica

Do[s=(Prime[n+1]-Prime[n])/Log[Prime[n]]//N; If[s>11, Print[{n, Prime[n], Prime[n+1], s, Log[Prime[n]]//N}]], {n, 1000000, 100000000}]

Crossrefs

Cf. A082862, A082884-A082890.

Sequence in context: A065590 A051249 A056165 * A000653 A128847 A123180

Adjacent sequences: A082888 A082889 A082890 * A082892 A082893 A082894

Keyword

more,nonn

Author

Labos Elemer, Apr 17 2003

Status

approved