A083848 a(n)^2 + 1 is largest prime of the form x^2 + 1 <= 2^n.

1, 1, 2, 2, 4, 6, 10, 14, 20, 26, 40, 56, 90, 126, 180, 250, 350, 496, 716, 1010, 1440, 2034, 2896, 4086, 5774, 8184, 11566, 16380, 23166, 32766, 46326, 65534, 92666, 131070, 185354, 262130, 370714, 524260, 741454, 1048554, 1482904, 2097146

Offset: 1

Author

Harry J. Smith, May 05 2003

Keywords

• nonn

Comments

It is conjectured that this sequence is infinite, but this has never been proved.

Ratio of successive terms appears to approach sqrt(2). - Bill McEachen, Nov 03 2013

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.

Crossrefs

Cf. A005574, A002496, A083844, A083845, A083846, A083847, A083849.