A178399 Primes p such that p is a quadratic residue modulo reverse(p) and reverse(p) is prime and a quadratic residue modulo p.

37, 73, 79, 97, 113, 149, 167, 311, 359, 389, 761, 941, 953, 983, 1009, 1021, 1031, 1033, 1069, 1097, 1109, 1153, 1181, 1193, 1201, 1213, 1231, 1237, 1283, 1301, 1321, 1453, 1619, 1753, 1811, 3049, 3121, 3169, 3301, 3319, 3347, 3359, 3373, 3511

Offset

1,1

Links

Table of n, a(n) for n=1..44.

Eric W. Weisstein, Quadratic Residue

Example

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).

Maple

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>

Crossrefs

Cf. A177873.

Sequence in context: A335484 A155087 A171807 * A044103 A044484 A158065

Adjacent sequences: A178396 A178397 A178398 * A178400 A178401 A178402

Keyword

nonn,base,less

Author

Michel Lagneau, Dec 21 2010

Status

approved