A203815 Primes which are the decimal concatenation of two squares in more than one way.

14449, 4651249, 14592449, 25281961, 64516961, 144552049, 4963984001, 10241442401, 121828921681, 1089936421201, 1589776384961, 4640334443681, 19713620187049, 25593280441009, 81105458016049, 121521961692601, 445309309225961

Offset

1,1

Comments

Subsequence of A167535.

Links

Table of n, a(n) for n=1..17.

Example

a(1) = 14449 = the concatenation of 12^2 and 7^2 and of 38^2 and 3^2.
a(5) = 64516961 = the concatenation of 8^2 and 719^2 and of 254^2 and 31^2.

Mathematica

K[m_Integer, n_Integer] := n+m*10^IntegerLength[n]; k=-1; V={}; g=5000000; W={}; While[k<g, k++; m=2 k+1; n=0; While[n<2 g, n++; a=K[n^2, m^2]; If[a>10 (2 g)^2, n=2 g, If[PrimeQ[a], V={V, a}]]]]; V=Flatten[V]; W1=Sort[V]; W2=Union[V](*= A167535*); i=0; While[i<Length[W1]-1, i++; If[W1[[i+1]]==W1[[i]], W=Append[W, W1[[i]]]]]; Union[W]

Crossrefs

Cf. A167535.

Sequence in context: A250960 A238060 A210050 * A076165 A234119 A253116

Adjacent sequences: A203812 A203813 A203814 * A203816 A203817 A203818

Keyword

nonn,base

Author

Emmanuel Vantieghem, Jan 06 2012

Status

approved