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 A269261 Record (maximal) gaps between primes of the form 10k + 9. 2
 10, 30, 80, 100, 110, 120, 170, 180, 190, 240, 270, 280, 290, 330, 360, 370, 500, 510, 610, 620, 630, 670, 700, 730, 840, 870, 950, 990, 1020, 1130, 1220, 1280, 1320, 1610, 1770, 1910, 2450 (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 + 9 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(A269263(n)) almost always. A269262 lists the primes preceding the maximal gaps. A269263 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 + 9 are 19 and 29, so a(1)=29-19=10. The next prime of this form is 59 and the gap 59-29=30 is a new record, so a(2)=30. PROG (PARI) re=0; s=19; forprime(p=29, 1e8, if(p%10!=9, next); g=p-s; if(g>re, re=g; print1(g", ")); s=p) CROSSREFS Cf. A030433, A269262, A269263. Sequence in context: A344333 A034127 A229466 * A328259 A005052 A057344 Adjacent sequences:  A269258 A269259 A269260 * A269262 A269263 A269264 KEYWORD nonn AUTHOR Alexei Kourbatov, Feb 20 2016 STATUS approved

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Last modified July 27 21:21 EDT 2021. Contains 346316 sequences. (Running on oeis4.)