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 A083849 a(n) is the largest prime of the form x^2 + 1 <= 2^n. 7
 2, 2, 5, 5, 17, 37, 101, 197, 401, 677, 1601, 3137, 8101, 15877, 32401, 62501, 122501, 246017, 512657, 1020101, 2073601, 4137157, 8386817, 16695397, 33339077, 66977857, 133772357, 268304401, 536663557, 1073610757, 2146098277 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS It is conjectured that this sequence is increasing, but this has never been proved. It is easily shown that all terms greater than 5 end in 1 or 7. REFERENCES G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, th. 17. P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, 1991, p. 190. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Landau's Problems. PROG (PARI) a(n) = my(last = 2^n+1); while ((p = precprime(last-1)) && (! issquare(p-1)), last = p; ); p \\ Michel Marcus, Jun 14 2013 (PARI) a(n)=my(k=sqrtint(2^n-1)); while(!isprime(k^2+1), k--); k^2+1 \\ Charles R Greathouse IV, Nov 29 2013 CROSSREFS Cf. A005574, A002496, A083844, A083845, A083846, A083847, A083848. Sequence in context: A245849 A245850 A245844 * A326512 A325983 A063501 Adjacent sequences:  A083846 A083847 A083848 * A083850 A083851 A083852 KEYWORD nonn AUTHOR Harry J. Smith, May 05 2003 STATUS approved

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Last modified February 19 00:35 EST 2020. Contains 332028 sequences. (Running on oeis4.)