A177872 Numbers k such that k is a quadratic residue modulo reverse(k) and reverse(k) is a quadratic residue modulo k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 22, 29, 33, 37, 38, 40, 44, 47, 51, 55, 56, 65, 66, 73, 74, 77, 78, 79, 83, 87, 88, 90, 92, 97, 99, 100, 101, 110, 111, 113, 117, 121, 124, 125, 131, 141, 143, 144, 146, 149, 151, 161, 163, 164, 167, 169, 171, 174, 181, 187, 189, 191, 198, 202, 209, 212, 222, 226, 232, 242, 252, 262, 263, 266

Offset

1,2

Links

Table of n, a(n) for n=1..76.

Example

a(17) = 38 is in the sequence because L(38/83)) = L(83/38) = 1, where L(a/b) is the Legendre symbol of a and b, which is defined to be 1 if a is a quadratic residue (mod b) and -1 if a is a quadratic non-residue (mod b) .

Maple

with(numtheory): for n from 1 to 300 do: s:=0:l:=length(n):for q from 0 to
  l-1 do:x:=iquo(n, 10^q):y:=irem(x, 10):s:=s+y*10^(l-1-q): od: if quadres(n, s)=1
  and quadres(s, n)=1 then printf(`%d, `, n):else fi:od:

Crossrefs

Sequence in context: A198323 A254649 A261293 * A271839 A290144 A115060

Adjacent sequences: A177869 A177870 A177871 * A177873 A177874 A177875

Keyword

nonn,base

Author

Michel Lagneau, Dec 13 2010

Status

approved