Search: id:A000230
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%I A000230 M2685
%S A000230 2,3,7,23,89,139,199,113,1831,523,887,1129,1669,2477,2971,4297,5591,
%T A000230 1327,9551,30593,19333,16141,15683,81463,28229,31907,19609,35617,
%U A000230 82073,44293,43331,34061,89689,162143,134513,173359,31397,404597,212701,
               188029,542603,265621,461717,155921,544279,404851,927869,1100977,360653,
               604073
%N A000230 Smallest prime p such that there is a gap of 2n between p and next prime.
%C A000230 The first term corresponds to a gap of 1 = 2*(1/2) (so the offset might 
               have been 1/2!).
%C A000230 a(n)=A000040(A038664(n)). - Lekraj Beedassy (blekraj(AT)yahoo.com), Sep 
               09 2006
%C A000230 Carella focuses on the problems of prime gaps and zero spacings. Possible 
               solutions of several related problems such as the greatest lower 
               bound, the least upper bound of the zero spacings, and the least 
               upper bound of the prime gaps are considered. [From Jonathan Vos 
               Post (jvospost3(AT)gmail.com), Mar 04 2009]
%D A000230 L. J. Lander and T. R. Parkin, On the first appearance of prime differences, 
               Math. Comp., 21 (1967), 483-488.
%D A000230 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000230 J. Young and A. Potler, First occurrence prime gaps, Math. Comp., 52 
               (1989), 221-224.
%H A000230 N. J. A. Sloane, <a href="b000230.txt">Table of n, a(n) for n=0..603</
               a> (from the web page of Tomas Oliveira e Silva)
%H A000230 A. Booker, <a href="http://primes.utm.edu/nthprime">The Nth Prime Page</
               a>
%H A000230 H. Bottomley, <a href="http://www.btinternet.com/~se16/js/prime.htm">
               Prime number calculator</a>
%H A000230 N. A. Carella, <a href="http://arxiv.org/abs/0903.0646">Note on Prime 
               Gaps and Zero Spacing</a>, Mar 3, 2009. [From Jonathan Vos Post (jvospost3(AT)gmail.com), 
               Mar 04 2009]
%H A000230 T. R. Nicely, <a href="http://www.trnicely.net/gaps/gaplist.html">List 
               of prime gaps</a>
%H A000230 Tomas Oliveira e Silva, <a href="http://www.ieeta.pt/~tos/gaps.html">
               Gaps between consecutive primes</a>
%H A000230 J. Thonnard, <a href="http://www.proftnj.com/calcprem.htm">Les nombres 
               premiers (Primality check; Closest next prime; Factorizer)</a>
%H A000230 <a href="Sindx_Pri.html#gaps">Index entries for primes, gaps between</
               a>
%e A000230 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);
%e A000230 * 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.
%e A000230 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.
%e A000230 -----
%e A000230 g P(g)
%e A000230 -----
%e A000230 1* 2*
%e A000230 2* 3*
%e A000230 4* 7*
%e A000230 6* 23*
%e A000230 8* 89*
%e A000230 10 139*
%e A000230 12 199*
%e A000230 14* 113
%e A000230 16 1831*
%e A000230 18* 523
%e A000230 20* 887
%e A000230 22* 1129
%e A000230 24 1669
%e A000230 26 2477*
%e A000230 28 2971*
%e A000230 30 4297*
%e A000230 32 5591*
%e A000230 34* 1327
%e A000230 36* 9551*
%e A000230 ........
%e A000230 The first time a gap of 4 occurs between primes is between 7 and 11, 
               so a(2)=7 and A001632(2)=11.
%t A000230 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
%Y A000230 A001632(n) = 2n + a(n) = nextprime(a(n)).
%Y A000230 Cf. A002386, A005250.
%Y A000230 Cf. A100964 (least prime number that begins a prime gap of at least 2n).
%Y A000230 For records see A133429, A133430, A100180.
%Y A000230 Sequence in context: A129739 A163834 A002386 this_sequence A133429 A087770 
               A087164
%Y A000230 Adjacent sequences: A000227 A000228 A000229 this_sequence A000231 A000232 
               A000233
%K A000230 nonn,nice
%O A000230 0,1
%A A000230 N. J. A. Sloane (njas(AT)research.att.com).
%E A000230 More terms from Jud McCranie j.mccranie(AT)comcast.net. Further terms 
               from Robert A. Stump (bee_ess107(AT)yahoo.com), Jan 11 2002

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