A104138 Smallest prime followed by n or more composites.

2, 3, 7, 7, 23, 23, 89, 89, 113, 113, 113, 113, 113, 113, 523, 523, 523, 523, 887, 887, 1129, 1129, 1327, 1327, 1327, 1327, 1327, 1327, 1327, 1327, 1327, 1327, 1327, 1327, 9551, 9551, 15683, 15683, 15683, 15683, 15683, 15683, 15683, 15683, 19609

Offset

0,1

Comments

Except for a(1), records occur at even values of n, and each term appears an even number of times consecutively. (Proof. A maximal run of composites must begin and end at even numbers.) - Jonathan Sondow, May 31 2014

Links

Charles R Greathouse IV, Table of n, a(n) for n = 0..1000

Formula

Record prime A002386(n+1) appears A053695(n-1) times, for n>1.

a(n) = A030296(n) - 1, for n > 0. - Jonathan Sondow, May 31 2014

Example

a(10)=113 because it is the first prime occurring before primes 199,211,293,317,467,509,... all followed by at least ten successive composites.

Crossrefs

Cf. A002386, A005250, A030296, A053695.

Sequence in context: A085420 A027672 A322138 * A281909 A083809 A092967

Adjacent sequences: A104135 A104136 A104137 * A104139 A104140 A104141

Keyword

nonn

Author

Lekraj Beedassy, Mar 07 2005

Extensions

a(34) corrected by Charles R Greathouse IV, Aug 09 2011

Status

approved