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A090190 Symmetric primes: an odd prime p is symmetric if there exists an odd prime q such that |p-q| = gcd(p-1,q-1).

%I A090190 #37 Nov 02 2022 14:26:01
%S A090190 3,5,7,11,13,17,19,29,31,37,41,43,53,59,61,67,71,73,79,89,97,101,103,
%T A090190 107,109,113,127,131,137,139,149,151,157,163,179,181,191,193,197,199,
%U A090190 211,223,227,229,233,239,241,251,257,269,271,277,281,283,293,307,311
%N A090190 Symmetric primes: an odd prime p is symmetric if there exists an odd prime q such that |p-q| = gcd(p-1,q-1).
%H A090190 Charles R Greathouse IV, <a href="/A090190/b090190.txt">Table of n, a(n) for n = 1..10000</a>
%H A090190 William Banks, Paul Pollack and Carl Pomerance, <a href="https://arxiv.org/abs/1908.06161">Symmetric primes revisited</a>, arXiv:1908.06161 [math.NT], 2019.
%H A090190 Rob Burns, <a href="https://arxiv.org/abs/2005.02922">Extremely symmetric primes</a>, arXiv:2005.02922 [math.NT], 2020.
%H A090190 P. Fletcher, W. Lindgren and C. Pomerance, <a href="https://doi.org/10.1006/jnth.1996.0066">Symmetric and asymmetric primes</a>, J. Number Theory 58 (1996) 89-99.
%H A090190 A. B. Kalmynin, <a href="http://math.colgate.edu/~integers/v2/v2.pdf">On the Symmetry Graph of Prime Numbers</a>, INTEGERS 21 (2021), #A2.
%e A090190 Any twin prime is symmetric since 2=gcd(p-1,p+1) for any odd prime p.
%t A090190 f[n_] := Block[{k = 2}, While[k < 10^3 && Abs[n - Prime[k]] != GCD[n - 1, Prime[k] - 1], k++ ]; If[k == 10^3, 0, Prime[k]]]; Select[ Prime[ Range[2, 100]], f[ # ] != 0 &] (* _Robert G. Wilson v_, Sep 19 2004 *)
%o A090190 (PARI) \\ Assumes n is an odd prime
%o A090190 is(p)=fordiv(p-1,d, if(isprime(p-d) || isprime(p+d), return(1))); 0 \\ _Charles R Greathouse IV_, Aug 24 2021
%Y A090190 Complement (in A000040) gives A090191.
%K A090190 nonn
%O A090190 1,1
%A A090190 _Steven Finch_, Jan 21 2004
%E A090190 More terms from _Robert G. Wilson v_, Sep 19 2004