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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
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
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
KEYWORD
nonn
AUTHOR
Harry J. Smith, May 05 2003
EXTENSIONS
More terms from Alexander D. Healy, Feb 06 2005
STATUS
approved