A161665 Primes that can be represented as a sum of 2 and also as a sum of 3 distinct nonzero squares, sharing a term in the sums.

29, 101, 109, 149, 173, 181, 229, 233, 241, 269, 293, 389, 401, 409, 421, 433, 449, 521, 569, 641, 661, 677, 701, 757, 761, 769, 797, 821, 857, 877, 881, 941, 1021, 1069, 1097, 1109, 1117, 1181, 1229, 1237, 1277, 1289, 1301, 1373, 1381, 1429, 1433, 1481, 1549

Offset

1,1

Comments

Dropping the requirement of one shared term, we would get the supersequence 17, 29, 41, 53, 61, 73, ... - R. J. Mathar, Oct 04 2009

Links

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

Example

The prime 29 has the representations 29 = 2^2+ 5^2 = 2^2+3^2+4^2, sharing 2^2.
The prime 101 has the representations 101 = 1^2+10^2 = 1^2+6^2+8^2, sharing 1^2.
The prime 109 has the representations 109 = 3^2+10^2 = 3^2+6^2+8^2, sharing 3^2.
The prime 149 has the representations 149 = 7^2+10^2 = 6^2+7^2+8^2, sharing 7^2.

Mathematica

f[n_]:=Module[{k=1}, While[(n-k^2)^(1/2)!=IntegerPart[(n-k^2)^(1/2)], k++; If[2*k^2>=n, k=0; Break[]]]; k]; lst={}; Do[a=f[n]; If[a>0, b=f[n-(f[n])^2]; If[b>0, c=(n-a^2-b^2)^(1/2); If[a!=b&&a!=c, If[PrimeQ[n], AppendTo[lst, n]]]]], {n, 3, 4*6!}]; lst

Crossrefs

Cf. A002114, A085317.

Sequence in context: A092373 A240954 A087641 * A127464 A318959 A142109

Adjacent sequences: A161662 A161663 A161664 * A161666 A161667 A161668

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jun 15 2009

Extensions

Definition reverse-engineered from program by R. J. Mathar, Oct 04 2009

Status

approved