0,1

The first term corresponds to a gap of 1 = 2*(1/2) (so the offset might have been 1/2!).

a(n)=A000040(A038664(n)). - Lekraj Beedassy (blekraj(AT)yahoo.com), Sep 09 2006

L. J. Lander and T. R. Parkin, On the first appearance of prime differences, Math. Comp., 21 (1967), 483-488.

J. Young and A. Potler, First occurrence prime gaps, Math. Comp., 52 (1989), 221-224.

N. J. A. Sloane, Table of n, a(n) for n=0..603 (from the web page of Tomas Oliveira e Silva)

A. Booker, The Nth Prime Page

H. Bottomley, Prime number calculator

T. R. Nicely, List of prime gaps

Tomas Oliveira e Silva, Gaps between consecutive primes

J. Thonnard, Les nombres premiers (Primality check; Closest next prime; Factorizer)

Index entries for primes, gaps between

The following table, based on a very much larger table in the web page of Tomas Oliveira e Silva (see link below) shows, for each gap g, P(g) = the smallest prime such that P(g)+g is the smallest prime number larger than P(g);

* marks a record-holder: g is a record-holder if P(g') > P(g) for all (even) g' > g, i.e. if all prime gaps are smaller than g for all primes smaller than P(g); P(g) is a record-holder if P(g') < P(g) for all (even) g' < g.

This table gives rise to many sequences: P(g) is A000230, the present sequence; P(g)* is A133430; the positions of the *'s in the P(g) column give A100180, A133430; g* is A005250; P(g*) is A002386; etc.

-----

g P(g)

-----

1* 2*

2* 3*

4* 7*

6* 23*

8* 89*

10 139*

12 199*

14* 113

16 1831*

18* 523

20* 887

22* 1129

24 1669

26 2477*

28 2971*

30 4297*

32 5591*

34* 1327

36* 9551*

........

The first time a gap of 4 occurs between primes is between 7 and 11, so a(2)=7 and A001632(2)=11.

a[n_] := If[n==1, 2, (For[m=1, Prime[m+1]-Prime[m]!= 2n-2, m++ ]; Prime[m])]; Table[a[n], {n, 50}] - from Farideh Firoozbakht (f.firoozbakht(AT)sci.ui.ac.irhea), Dec 17 2003

A001632(n) = 2n + a(n) = nextprime(a(n)).

Cf. A002386, A005250.

Cf. A100964 (least prime number that begins a prime gap of at least 2n).

For records see A133429, A133430, A100180.

Adjacent sequences: A000227 A000228 A000229 this_sequence A000231 A000232 A000233

Sequence in context: A088173 A129739 A002386 this_sequence A133429 A087770 A087164

nonn,nice

njas

More terms from Jud McCranie j.mccranie(AT)comcast.net. Further terms from Robert A. Stump (bee_ess107(AT)yahoo.com), Jan 11 2002