A027833 Distances between successive 2's in sequence A001223 of differences between consecutive primes.

1, 2, 2, 3, 3, 4, 3, 6, 2, 5, 2, 6, 2, 2, 4, 3, 5, 3, 4, 5, 12, 2, 6, 9, 6, 5, 4, 3, 4, 20, 2, 2, 4, 4, 19, 2, 3, 2, 4, 8, 11, 5, 3, 3, 3, 10, 5, 4, 2, 17, 3, 6, 3, 3, 9, 9, 2, 6, 2, 6, 5, 6, 2, 3, 2, 3, 9, 4, 7, 3, 7, 20, 4, 7, 6, 5, 3, 7, 3, 20, 2, 14, 4, 10, 2, 3, 6, 4, 2, 2, 7, 2, 6, 3

Offset

1,2

Comments

a(n) = number of primes p such that A014574(n) < p < A014574(n+1). - Thomas Ordowski, Jul 20 2012

Conjecture: a(n) < log(A014574(n))^2. - Thomas Ordowski, Jul 21 2012

Conjecture: All positive integers are represented in this sequence. This is verified up to 184, by searching up to prime indexes of ~128000000. The rate of filling-in the smallest remaining gap among the integers, and the growth in the maximum value found, both slow down considerably relative to a fixed quantity of twin prime incidences examined in each pass. The maximum value found was 237. - Richard R. Forberg, Jul 28 2016

All positive integers below 312 are in this sequence. - Charles R Greathouse IV, Aug 01 2016

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Mathematica

Differences[Flatten[Position[Differences[Prime[Range[500]]], 2]]] (* Harvey P. Dale, Nov 17 2018 *)

Prog

(Sage)
def A027833(n) :
   a = [ ]
   st = 2
   for i in (3..n) :
      if (nth_prime(i+1)-nth_prime(i) == 2) :
         a.append(i-st)
         st = i
   return(a)
A027833(496) # Jani Melik, May 15 2014
(PARI) n=1; p=5; forprime(q=7, 1e3, if(q-p==2, print1(n", "); n=1, n++); p=q) \\ Charles R Greathouse IV, Aug 01 2016

Crossrefs

Cf. A001223.

First differences of A029707 and A155752 = A029707 - 1. M. F. Hasler, Jul 24 2012

Sequence in context: A182921 A291268 A242767 * A110676 A117171 A325356

Adjacent sequences: A027830 A027831 A027832 * A027834 A027835 A027836

Keyword

nonn

Author

Jean-Marc MALASOMA (Malasoma(AT)entpe.fr)

Status

approved