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 A178399 Primes p such that p is a quadratic residue modulo reverse(p) and reverse(p) is prime and a quadratic residue modulo p. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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:

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

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Last modified September 30 07:44 EDT 2023. Contains 365781 sequences. (Running on oeis4.)