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A083845 a(n)^2 + 1 is largest prime of the form x^2 + 1 <= 10^n. 4
2, 6, 26, 94, 314, 986, 3160, 9990, 31614, 99996, 316206, 999960, 3162246, 9999960, 31622764, 99999966, 316227734, 999999924, 3162277654, 9999999956, 31622776500, 99999999964, 316227766006, 999999999886, 3162277660140 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

It is conjectured that the number of primes of the form x^2+1 is infinite and thus this sequence never becomes a constant, but this has not been proved.

The ratio a(n+2)/a(n) appears to approach 10, as one might expect. - 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

Table of n, a(n) for n=1..25.

Eric Weisstein's World of Mathematics, Landau's Problems.

MATHEMATICA

Do[ k = Floor[ Sqrt[ 10^n] - 1]; While[ !PrimeQ[k^2 + 1], k-- ]; Print[k], {n, 1, 25}]

CROSSREFS

Cf. A005574, A002496, A083844, A083846, A083847, A083848, A083849.

Sequence in context: A240296 A027207 A027231 * A027239 A191821 A290958

Adjacent sequences:  A083842 A083843 A083844 * A083846 A083847 A083848

KEYWORD

nonn

AUTHOR

Harry J. Smith, May 05 2003

EXTENSIONS

Edited and extended by Robert G. Wilson v, May 08 2003

STATUS

approved

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Last modified January 20 02:29 EST 2018. Contains 297938 sequences.