login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A174222 Number of symmetric primes in the interval [prime(n)^2, prime(n)*prime(n+1)]. 0
1, 2, 2, 6, 4, 7, 5, 10, 18, 6, 24, 18, 10, 21, 35, 29, 14, 33, 27, 14, 44, 32, 43, 64, 36, 16, 36, 17, 38, 133, 41, 71, 16, 123, 21, 71, 72, 49, 90, 85, 36, 158, 34, 66, 31, 190, 184, 73, 39, 73, 109, 33, 188, 109, 117, 110, 35, 126, 85, 36, 221, 298, 99, 41, 95, 320, 136, 237 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If you graph a(n) vs. n, an interesting pattern with random-looking fluctuations begins to emerge.

As you go farther along the n-axis, greater are the number of Symmetric primes, on average.

The smallest count of a(.)=1 occurs only once at the very beginning.

I suspect all a(n) are > 0. If one could prove this, it would imply that Symmetric primes are infinite.

LINKS

Table of n, a(n) for n=1..68.

FORMULA

#{ A090190(j): A001248(n) < A090190(j) < A006094(n)}.

EXAMPLE

The square of the first prime is 2^2=4 and the product of the first and second prime is 2*3=6. Within this interval, there is 1 Symmetric Prime, which is 5. Hence a(1)=1.

The second term, a(2)=2, refers to the two Symmetric primes 11 and 13 within the interval (9,15).

CROSSREFS

Cf. A090190, A090191

Sequence in context: A182411 A067804 A074911 * A071059 A061108 A053213

Adjacent sequences:  A174219 A174220 A174221 * A174223 A174224 A174225

KEYWORD

nonn

AUTHOR

Jaspal Singh Cheema (Jaspal(AT)rogers.com), Mar 18 2010

EXTENSIONS

Edited by R. J. Mathar, Mar 31 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 28 08:29 EST 2014. Contains 250285 sequences.