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 A057206 Primes of the form 6k+5 generated recursively: a(1)=5; a(n) = min{p, prime; p mod 6 = 5; p | 6Q-1}, where Q is the product of all previous terms in the sequence. 2
 5, 29, 11, 1367, 13082189, 89, 59, 29819952677, 91736008068017, 17, 887050405736870123700827, 688273423680369013308306870159348033807942418302818522537, 74367405177105011, 12731422703, 1812053 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS There are infinitely many primes of the form 6k + 5, and this sequence figures in the classic proof of that fact. - Alonso del Arte, Mar 02 2017 REFERENCES Dirichlet, P. G. L. (1871): Vorlesungen uber Zahlentheorie. Braunschweig, Viewig, Supplement VI, 24 pages. G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, page 13. LINKS Robert Price, Table of n, a(n) for n = 1..17 EXAMPLE a(3) = 11 is the smallest prime divisor of the form 6k + 5 of 6 * (5 * 29) - 1 = 6Q - 1 = 11 * 79 = 869. MATHEMATICA primes5mod6 = {5}; q = 1; For[n = 2, n <= 10, n++, q = q * Last[ primes5mod6]; AppendTo[primes5mod6, Min[Select[FactorInteger[6 * q - 1][[All, 1]], Mod[#, 6] == 5 &]]]; ]; primes5mod6 (* Robert Price, Jul 18 2015 *) PROG (PARI) main(size)={my(v=vector(size), i, q=1, t); for(i=1, size, t=1; while(!(prime(t)%6==5&&(6*q-1)%prime(t)==0), t++); v[i]=prime(t); q*=v[i]); v; } /* Anders HellstrÃ¶m, Jul 18 2015 */ CROSSREFS Cf. A000945, A000946, A005265, A005266, A051308-A051335, A057204-A057208, A007528. Sequence in context: A083020 A033503 A181616 * A057713 A124987 A002584 Adjacent sequences:  A057203 A057204 A057205 * A057207 A057208 A057209 KEYWORD nonn AUTHOR Labos Elemer, Oct 09 2000 EXTENSIONS a(13)-a(17) from Robert Price, Jul 18 2015 STATUS approved

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Last modified May 31 15:41 EDT 2020. Contains 334748 sequences. (Running on oeis4.)