A178399 - OEIS

%I #12 Mar 30 2012 18:35:53

%S 37,73,79,97,113,149,167,311,359,389,761,941,953,983,1009,1021,1031,

%T 1033,1069,1097,1109,1153,1181,1193,1201,1213,1231,1237,1283,1301,

%U 1321,1453,1619,1753,1811,3049,3121,3169,3301,3319,3347,3359,3373,3511

%N Primes p such that p is a quadratic residue modulo reverse(p) and reverse(p) is prime and a quadratic residue modulo p.

%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/QuadraticResidue.html">Quadratic Residue</a>

%e The prime 1237 in the sequence because L(1237/7321) = L(7321/1237) = 1, with 7321 also prime, where L(a/p) = 1 if a is a quadratic residue modulo p and a <> 0 (mod p); L(a/p) = - 1 if a quadratic non-residue residue modulo p ; L(a/p) = 0 if a = 0 (mod p).

%p for n from 1 to 5000 do: s:=0:l:=length(n):for q from 0 to l do:x:=iquo(n, 10^q):y:=irem(x, 10):s:=s+y*10^(l-1-q): od: if s<>n and quadres(n,s)=1 and quadres(s,  n)=1 and type(n, prime)=true and type(s, prime)=true then printf(`%d, `, n):else  fi:od: </p>

%Y Cf. A177873.

%K nonn,base,less

%O 1,1

%A _Michel Lagneau_, Dec 21 2010