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 A269234 Record (maximal) gaps between primes of the form 10k + 3. 2
 10, 20, 50, 70, 80, 90, 100, 110, 120, 130, 150, 300, 360, 420, 500, 510, 540, 550, 610, 630, 650, 690, 780, 810, 820, 840, 870, 890, 960, 990, 1280, 1370, 1380, 1470, 1690 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Dirichlet's theorem on arithmetic progressions suggests that average gaps between primes of the form 10k + 3 below x are about phi(10)*log(x). This sequence shows that the record gap ending at p grows almost as fast as phi(10)*log^2(p). Here phi(n) is A000010, Euler's totient function; phi(10)=4. Conjecture: a(n) < phi(10)*log^2(A269236(n)) almost always. A269235 lists the primes preceding the maximal gaps. A269236 lists the corresponding primes at the end of the maximal gaps. LINKS Alexei Kourbatov, On the distribution of maximal gaps between primes in residue classes, arXiv:1610.03340 [math.NT], 2016. Alexei Kourbatov, On the nth record gap between primes in an arithmetic progression, arXiv:1709.05508 [math.NT], 2017; Int. Math. Forum, 13 (2018), 65-78. Alexei Kourbatov and Marek Wolf, Predicting maximal gaps in sets of primes, arXiv preprint arXiv:1901.03785 [math.NT], 2019. EXAMPLE The first two primes of the form 10k + 3 are 3 and 13, so a(1)=13-3=10. The next prime of this form is 23; the gap 23-13 is not a record so nothing is added to the sequence. The next prime of this form is 43 and the gap 43-23=20 is a new record, so a(2)=20. PROG (PARI) re=0; s=3; forprime(p=13, 1e8, if(p%10!=3, next); g=p-s; if(g>re, re=g; print1(g", ")); s=p) CROSSREFS Cf. A030431, A269235, A269236. Sequence in context: A007927 A284991 A327692 * A160517 A072081 A034087 Adjacent sequences:  A269231 A269232 A269233 * A269235 A269236 A269237 KEYWORD nonn AUTHOR Alexei Kourbatov, Feb 20 2016 STATUS approved

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Last modified November 17 11:02 EST 2019. Contains 329226 sequences. (Running on oeis4.)