A046933 Number of composites between successive primes.

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

Offset

1,4

Comments

a(n) is odd for n>1 since all primes except 2 are odd. - Joel Brennan, Jan 02 2023

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.

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

a(n) = 2*A028334(n) - 1 for n>1. - Giovanni Teofilatto, Apr 19 2010

a(n) = Sum_{i=1..n-1} A036263(i). - 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 *)
Prepend[Drop[Length/@SequenceSplit[Range@Prime@100, {_?PrimeQ}], 1], 0] (* Federico Provvedi, Jul 19 2021 *)

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
(Python)
from sympy import prime
def A046933(n): return prime(n+1)-prime(n)-1 # Chai Wah Wu, Jan 02 2024

Crossrefs

Cf. A000040, A028334, A036263.

Cf. A008996 (record values > 0).

Sequence in context: A066839 A372832 A176246 * A185091 A332031 A023511

Adjacent sequences: A046930 A046931 A046932 * A046934 A046935 A046936

Keyword

easy,nonn,nice

Author

Marc LeBrun, Dec 11 1999

Status

approved