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A027833 Distances between successive 2's in sequence A001223 of differences between consecutive primes. 7
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 16 17:04 EST 2019. Contains 329201 sequences. (Running on oeis4.)