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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 24 20:09 EDT 2018. Contains 315356 sequences. (Running on oeis4.)