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Least number which is the end of an arithmetic progression of n numbers that are the sums of two nonzero squares.
1

%I #5 Mar 31 2012 10:29:04

%S 2,5,8,26,34,65,146,170,194,218,242,1445,2225,2309,2393,2477,2561,

%T 2645,2729,2813,2897,71633,479581,664445,685697,1141625,1184129,

%U 4281133,4344889,4408645,31694041,32519173,33344305

%N Least number which is the end of an arithmetic progression of n numbers that are the sums of two nonzero squares.

%C The next term is > 225000000.

%H Ben Green and Terence Tao, <a href="http://arXiv.org/abs/math/0404188">The primes contain arbitrarily long arithmetic progressions</a>

%e Example: a(6)=65: 5=2^2+1^2, 17=4^2+1^2, 29=5^2+2^2, 41=5^2+4^2, 53=7^2+2^2, 65=7^2+4^2.

%Y Arithmetic progressions in A000404. For gaps see A093366.

%Y Cf. A005115, arithmetic progressions of primes.

%K nonn

%O 1,1

%A _Hugo Pfoertner_, Apr 27 2004

%E More terms from _Hugo Pfoertner_, Apr 29 2004

%E Corrected erroneous terms starting at a(28) _Hugo Pfoertner_, Oct 15 2010