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A196274 Half of the gaps A067970 between odd nonprimes A014076. 6
4, 3, 3, 2, 1, 3, 1, 2, 3, 2, 1, 2, 1, 3, 1, 2, 3, 1, 2, 2, 1, 2, 1, 1, 2, 3, 3, 2, 1, 1, 1, 1, 1, 2, 2, 1, 3, 1, 1, 1, 3, 1, 2, 1, 2, 2, 1, 2, 1, 3, 1, 1, 1, 3, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 3, 2, 1, 3, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 3, 1, 1, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) < 4 for n > 1; a(A196276(a(n)) = 1; a(A196277(a(n)) > 1. [Reinhard Zumkeller, Sep 30 2011]

Lengths of runs of equal terms in A025549. That sequence begins with: 1,1,1,1,3,3,3,45,45,45,..., that is 4 ones, 3 threes, 3 forty-fives, ... - Michel Marcus, Dec 02 2014

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = (A014076(n+1)-A014076(n))/2 = A067970(n)/2.

EXAMPLE

The smallest odd numbers which are not prime are 1, 9, 15, 21, 25, 27,... (sequence A014076).

The gaps between these are: 8, 6, 6, 4, 2,... (sequence A067970), which are of course all even by construction, so it makes sense to divide all of them by 2, which yields this sequence: 4, 3, 3, 2, 1, ...

MATHEMATICA

With[{nn=401}, Differences[Complement[Range[1, nn, 2], Prime[Range[ PrimePi[ nn]]]]]/2] (* Harvey P. Dale, May 06 2012 *)

PROG

(PARI) L=1; forstep(n=3, 299, 2, isprime(n)&next; print1((n-L)/2", "); L=n)

CROSSREFS

Cf. A142723 for the decimal value of the associated continued fraction.

Sequence in context: A177038 A019975 A327869 * A073871 A120927 A241180

Adjacent sequences:  A196271 A196272 A196273 * A196275 A196276 A196277

KEYWORD

nonn

AUTHOR

M. F. Hasler, Sep 30 2011

EXTENSIONS

More terms from Harvey P. Dale, May 06 2012

STATUS

approved

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Last modified October 19 13:01 EDT 2019. Contains 328222 sequences. (Running on oeis4.)