A177873 Primes p such that p is a quadratic residue modulo reverse(p) and reverse(p) is a quadratic residue modulo p.

29, 37, 47, 73, 79, 83, 97, 113, 149, 163, 167, 263, 277, 283, 311, 317, 349, 359, 389, 421, 433, 449, 461, 509, 521, 607, 617, 641, 761, 941, 953, 983, 1009, 1021, 1031, 1033, 1069, 1097, 1109, 1153, 1181, 1193, 1201, 1213, 1231, 1237, 1283, 1301, 1321

Offset

1,1

Comments

Primes in A177872, excluding the palindromic primes A002385.

Links

Table of n, a(n) for n=1..49.

Eric W. Weisstein, Quadratic Residue

Eric W. Weisstein, Jacobi Symbol

Example

Prime 317 is in the sequence because J(317, 713) = J(713, 317) = 1 where J is the Jacobi symbol.

Maple

with(numtheory): for n from 1 to 2500 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 then printf(`%d, `, n):else fi:od:

Crossrefs

Cf. A177872, A178399.

Sequence in context: A255204 A049746 A097997 * A234973 A134100 A060769

Adjacent sequences: A177870 A177871 A177872 * A177874 A177875 A177876

Keyword

nonn,base

Author

Michel Lagneau, Dec 13 2010

Status

approved