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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

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Last modified October 2 12:40 EDT 2014. Contains 247541 sequences.