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A046933 Number of composites between successive primes. 35
0, 1, 1, 3, 1, 3, 1, 3, 5, 1, 5, 3, 1, 3, 5, 5, 1, 5, 3, 1, 5, 3, 5, 7, 3, 1, 3, 1, 3, 13, 3, 5, 1, 9, 1, 5, 5, 3, 5, 5, 1, 9, 1, 3, 1, 11, 11, 3, 1, 3, 5, 1, 9, 5, 5, 5, 1, 5, 3, 1, 9, 13, 3, 1, 3, 13, 5, 9, 1, 3, 5, 7, 5, 5, 3, 5, 7, 3, 7, 9, 1, 9, 1, 5, 3, 5, 7, 3, 1, 3, 11, 7, 3, 7, 3, 5, 11, 1, 17 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

n-th odd number of A028334(k). - Giovanni Teofilatto, Apr 19 2010

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = prime(n+1) - prime(n) - 1 = A000040(n+1) - A000040(n) - 1, n >= 1.

a(n) = A001223(n) - 1, n >= 1.

a(n) = sum(i=1..n-1, A036263(i)), n >= 1. - Daniel Forgues, Apr 07 2014

EXAMPLE

a(1) = 0 since 2 is adjacent to 3; a(2) = 1 since 4 is between 3 and 5; a(4) = 3 = 11 - 7 - 1, etc

MAPLE

A046933:=n->ithprime(n+1)-ithprime(n)-1; seq(A046933(n), n=1..100); # Wesley Ivan Hurt, Apr 15 2014

MATHEMATICA

Differences[Prime[Range[100]]] - 1 (* Arkadiusz Wesolowski, Nov 18 2011 *)

Table[Prime[n + 1] - Prime[n] - 1, {n, 100}] (* Wesley Ivan Hurt, Apr 15 2014 *)

PROG

(PARI) a(n)=prime(n+1)-prime(n)-1 \\ Charles R Greathouse IV, Nov 20 2012

(Haskell)

a046933 n = a046933_list !! (n-1)

a046933_list = map (subtract 1) a001223_list

-- Reinhard Zumkeller, Dec 12 2012

CROSSREFS

Cf. A028334.

Cf. A008996 (record values > 0).

Sequence in context: A109599 A066839 A176246 * A185091 A023511 A035628

Adjacent sequences:  A046930 A046931 A046932 * A046934 A046935 A046936

KEYWORD

easy,nonn,nice

AUTHOR

Marc LeBrun, Dec 11 1999

STATUS

approved

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Last modified January 20 21:36 EST 2019. Contains 319336 sequences. (Running on oeis4.)