

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
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OFFSET

1,2


COMMENTS

If you graph a(n) vs. n, an interesting pattern with randomlooking fluctuations begins to emerge.
As you go farther along the naxis, 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 A256468 A061108
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



