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 A083847 a(n) = number of primes of the form x^2 + 1 <= 2^n. 6
 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 14, 18, 24, 33, 42, 54, 70, 91, 114, 158, 212, 293, 393, 539, 713, 957, 1301, 1792, 2459, 3378, 4615, 6233, 8418, 11540, 15867, 21729, 29843, 41169, 56534, 77697, 106787, 147067, 203025, 280340, 387308, 535153, 739671, 1023655, 1416635, 1960813, 2716922, 3764693, 5218926, 7238715 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS It is conjectured that the number of primes of the form x^2+1 is infinite and thus this sequence does not become a constant, but this has never been proved. 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 C. K. Caldwell, An amazing prime heuristic. Eric Weisstein's World of Mathematics, Landau's Problems. PROG (PARI) a(n) = my(nb = 0); forprime(p=2, 2^n, if (issquare(p-1), nb++); ); nb  \\ Michel Marcus, Jun 14 2013 CROSSREFS Cf. A005574, A002496, A083844 - A083849. Sequence in context: A114097 A325855 A174246 * A034142 A008675 A027581 Adjacent sequences:  A083844 A083845 A083846 * A083848 A083849 A083850 KEYWORD nonn AUTHOR Harry J. Smith, May 05 2003 EXTENSIONS More terms from Alex Healy, Feb 06 2005 STATUS approved

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Last modified October 16 20:55 EDT 2019. Contains 328103 sequences. (Running on oeis4.)