

A014689


a(n) = prime(n)n, the number of nonprimes less than prime(n).


56



1, 1, 2, 3, 6, 7, 10, 11, 14, 19, 20, 25, 28, 29, 32, 37, 42, 43, 48, 51, 52, 57, 60, 65, 72, 75, 76, 79, 80, 83, 96, 99, 104, 105, 114, 115, 120, 125, 128, 133, 138, 139, 148, 149, 152, 153, 164, 175, 178, 179, 182, 187, 188, 197, 202, 207, 212, 213, 218, 221, 222
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OFFSET

1,3


COMMENTS

a(n) = A048864(A000040(n)) = number of nonprimes in RRS of nth prime.  Labos Elemer, Oct 10 2002
A000040  A014689 = A000027; in other words, the sequence of natural numbers subtracted from the prime sequence produces A014689.  Enoch Haga, May 25 2009
a(n) = A000040(n)  n. a(n) = inverse (frequency distribution) sequence of A073425(n), i.e., number of terms of sequence A073425(n) less than n. a(n) = A065890(n) + 1, for n >= 1. a(n)  1 = A065890(n) = the number of composite numbers, i.e., (A002808) less than nth primes, (i.e., < A000040(n)).  Jaroslav Krizek, Jun 27 2009
a(n) = A162177(n+1) + 1, for n >= 1. a(n)  1 = A162177(n+1) = the number of composite numbers, i.e., (A002808) less than (n+1)th number of set {1, primes}, (i.e., < A008578(n+1)).  Jaroslav Krizek, Jun 28 2009
Conjecture: Each residue class contains infinitely many terms of this sequence. Similarly, for any integers m > 0 and r, we have prime(n) + n == r (mod m) for infinitely many positive integers n.  ZhiWei Sun, Nov 25 2013
First differences are A046933 = differences minus one between successive primes.  Gus Wiseman, Jan 18 2020


LINKS

T. D. Noe, Table of n, a(n) for n=1..1000


FORMULA

G.f: b(x)  x/((1x)^2), where b(x) is the g.f. of A000040.  Mario C. Enriquez, Dec 13 2016


MATHEMATICA

Table[Prime[n]  n, {n, 61}] (* Alonso del Arte *)


PROG

(PARI) a(n) = prime(n)n \\ Charles R Greathouse IV, Sep 05 2011
(Haskell)
a014689 n = a000040 n  fromIntegral n
 Reinhard Zumkeller, Apr 09 2012
(MAGMA) [NthPrime(n)n: n in [1..70]]; // Vincenzo Librandi, Mar 20 2013


CROSSREFS

Equals A014692  1.
Cf. A000040, A033286, A158611, A002808, A065890.
Cf. A232463, A232443.
The sum of prime factors of n is A001414(n).
The sum of prime indices of n is A056239(n).
Their difference is A331415(n).
Cf. A000720, A046933, A056239, A318995, A325036, A331380, A331416, A331418.
Sequence in context: A190670 A226115 A073170 * A117206 A026443 A204323
Adjacent sequences: A014686 A014687 A014688 * A014690 A014691 A014692


KEYWORD

nonn,easy,nice


AUTHOR

Mohammad K. Azarian


EXTENSIONS

More terms from Vasiliy Danilov (danilovv(AT)usa.net), July 1998
Correction for Aug 2009 change of offset in A158611 and A008578 by Jaroslav Krizek, Jan 27 2010


STATUS

approved



