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A100486 a(n) = pi(n) + n-th 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 (list; graph; refs; listen; history; text; internal format)
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: A099847 A014817 A090893 * A139533 A227116 A180742

Adjacent sequences:  A100483 A100484 A100485 * A100487 A100488 A100489

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Nov 22 2004

STATUS

approved

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Last modified February 21 11:36 EST 2019. Contains 320372 sequences. (Running on oeis4.)