This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A174222 #7 Nov 03 2022 07:42:39
%S A174222 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,
%T A174222 16,36,17,38,133,41,71,16,123,21,71,72,49,90,85,36,158,34,66,31,190,
%U A174222 184,73,39,73,109,33,188,109,117,110,35,126,85,36,221,298,99,41,95,320,136,237
%N A174222 Number of symmetric primes in the interval [prime(n)^2, prime(n)*prime(n+1)].
%C A174222 If you graph a(n) vs. n, an interesting pattern with random-looking fluctuations begins to emerge.
%C A174222 As you go farther along the n-axis, greater are the number of symmetric primes, on average.
%C A174222 The smallest count of a(.)=1 occurs only once at the very beginning.
%C A174222 I suspect all a(n) are > 0. If one could prove this, it would imply that Symmetric primes are infinite.
%F A174222 #{ A090190(j): A001248(n) < A090190(j) < A006094(n)}.
%e A174222 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.
%e A174222 The second term, a(2)=2, refers to the two symmetric primes 11 and 13 within the interval (9,15).
%o A174222 (PARI) issym(p) = fordiv(p-1, d, if(isprime(p-d) || isprime(p+d), return(1))); 0; \\ A090190
%o A174222 a(n) = my(p=prime(n), nb=0); forprime(q=p^2, p*nextprime(p+1), if (issym(q), nb++)); nb; \\ _Michel Marcus_, Nov 03 2022
%Y A174222 Cf. A090190, A090191.
%Y A174222 Cf. A006094, A001248,
%K A174222 nonn
%O A174222 1,2
%A A174222 _Jaspal Singh Cheema_, Mar 18 2010
%E A174222 Edited by _R. J. Mathar_, Mar 31 2010