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A014689 a(n) = prime(n)-n, the number of nonprimes less than prime(n). 45
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n) = A048864(A000040(n)) = number of nonprimes in RRS of n-th 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 n-th 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. - Zhi-Wei Sun, Nov 25 2013

LINKS

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

FORMULA

G.f: b(x) - x/((1-x)^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.

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

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Last modified February 20 22:51 EST 2019. Contains 320362 sequences. (Running on oeis4.)