

A100486


a(n) = pi(n) + nth prime, where pi(n) = A000720(n) is the prime counting function.


4



2, 4, 7, 9, 14, 16, 21, 23, 27, 33, 36, 42, 47, 49, 53, 59, 66, 68, 75, 79, 81, 87, 92, 98, 106, 110, 112, 116, 119, 123, 138, 142, 148, 150, 160, 162, 169, 175, 179, 185, 192, 194, 205, 207, 211, 213, 226, 238, 242, 244, 248, 254, 257, 267, 273, 279, 285, 287
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OFFSET

1,1


COMMENTS

This sequence is asymptotic to Li(n) + n/log(n). Conjecture: it contains infinitely many primes, beginning with 2, 7, 23, 47, 53, 59, 79, 179, 211, 257.


REFERENCES

Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, 1993.


LINKS

Indranil Ghosh, Table of n, a(n) for n = 1..10410
Andrew Booker, The Nth Prime Page.
Eric Weisstein's World of Mathematics, "Prime Counting Function."


FORMULA

a(n) = A000720(n) + A000040(n).  Wesley Ivan Hurt, Jan 28 2014


EXAMPLE

a(21) = 81 because a(21) = pi(21) + 21st prime = 8 + 73 = 81.


MAPLE

with(numtheory); A100486:=n>pi(n) + ithprime(n); seq(A100486(n), n=1..60); # Wesley Ivan Hurt, Jan 28 2014


MATHEMATICA

Table[PrimePi[n] + Prime[n], {n, 60}]


CROSSREFS

Cf. A000040, A000720, A065042, A100917.
Sequence in context: A014817 A326502 A090893 * A139533 A227116 A180742
Adjacent sequences: A100483 A100484 A100485 * A100487 A100488 A100489


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Nov 22 2004


STATUS

approved



