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A033168 Longest arithmetic progression of primes with difference 210 and minimal initial term.

%I A033168 #40 Sep 15 2024 02:16:01
%S A033168 199,409,619,829,1039,1249,1459,1669,1879,2089
%N A033168 Longest arithmetic progression of primes with difference 210 and minimal initial term.
%C A033168 Since 210 == 1 (mod 11), a progression of primes with difference 210 can't have more than ten terms because there is exactly one multiple of 11 within each run of eleven consecutive terms. For example, 2089 + 210 = 2299 = 11^2 * 19. - _Alonso del Arte_, Dec 22 2017, edited by _M. F. Hasler_, Jan 02 2020
%C A033168 After 199, the next prime which starts a CPAP-10 with common gap 210 is 243051733. See A094220 for further starting points. - _M. F. Hasler_, Jan 02 2020
%D A033168 Paul Glendinning, Math in Minutes: 200 Key Concepts Explained in an Instant. New York, London: Quercus (2013): pp. 316-317.
%D A033168 David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 143.
%H A033168 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/NonRecursions.html">Non Recursions</a>.
%H A033168 OEIS wiki, <a href="https://oeis.org/wiki/Primes_in_arithmetic_progression">Primes in arithmetic progression</a>.
%H A033168 <a href="/index/Pri#primes_AP">Index entries for sequences related to primes in arithmetic progressions</a>.
%F A033168 a(n) = a(0) + n*210 for 0 <= n <= 9. - _M. F. Hasler_, Jan 02 2020
%t A033168 199 + 210*Range[0, 9] (* _Paolo Xausa_, Sep 14 2024 *)
%o A033168 (PARI) forprime(p=1,,for(i=1,9,isprime(p+i*210)||next(2)); return([p+d|d<-[0..9]*210])) \\ _M. F. Hasler_, Jan 02 2020
%Y A033168 Row 10 of A086786, A113470, A133276, A133277.
%Y A033168 Cf. A094220.
%K A033168 nonn,fini,full
%O A033168 0,1
%A A033168 _Manuel Valdivia_, Apr 22 1998