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A179076 Number of primes of the form k^2 + 1 less than n. 0
0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

The first n such that a(n) = 5 is a(102). Records in a(n) are a(n) = A002496(n)+1. Hardy and Littlewood conjectured that, asymptotically, a(n) ~ c*(sqrt(n))/log n, where c ~ 1.3727.

REFERENCES

Richard K. Guy, Unsolved Problems in Number Theory, 2nd Edn., Springer, 1994, A1, pp.4-5.

LINKS

Table of n, a(n) for n=1..105.

EXAMPLE

a(3) = 1 because the unique prime of the form k^2 + 1 less than 3 is 1^2 + 1 = 2. The smallest value of n to reach the next record is a(6) = 2 because a(18) = 2, the two primes of the form k^2 + 1 less than 6 are 2 and 2^2 + 1 = 5. The smallest value of n to reach the next record is a(18) = 3 because the three primes of the form k^2 + 1 less than 18 are 2, 5, and 4^2 + 1 = 17.

CROSSREFS

Cf. A000040, A002496.

Sequence in context: A156877 A110591 A105209 * A095861 A111855 A071701

Adjacent sequences:  A179073 A179074 A179075 * A179077 A179078 A179079

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Jun 28 2010

STATUS

approved

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Last modified February 22 09:22 EST 2020. Contains 332133 sequences. (Running on oeis4.)