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A272069 Odd numbers n such that 3^n+1 is a sum of two squares. 0

%I

%S 1,5,13,65,149,281,409,421,449,461,577,761

%N Odd numbers n such that 3^n+1 is a sum of two squares.

%C Keenan Curtis found the values up though 577 in his undergraduate thesis (working with Jeremy Rouse at Wake Forest University). Keenan proved that if 3^n+1 is a sum of two squares for n odd, then n must be equivalent to 1 mod 4, that n itself is a sum of two squares, and that 3^p+1 is a sum of two squares for all primes p dividing n.

%D Keenan Curtis, "Sums of Two Squares: An Analysis of Numbers of the form 2^n+1 and 3^n+1", submitted to INVOLVE.

%H Greg Dresden, Kylie Hess, Saimon Islam, Jeremy Rouse, Aaron Schmitt, Emily Stamm, Terrin Warren, Pan Yue, <a href="https://arxiv.org/abs/1609.04391">When is a^n+1 the sum of two squares?</a>, arXiv:1609.04391 [math.NT], 2016. See p. 20.

%H S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/cun/index.html">The Cunningham Project</a>

%e 3^1+1 = 4 = 0^2 + 2^2, so 1 is a term;

%e 3^5+1 = 244 = 10^2 + 12^2, so 5 is a term;

%e 3^13+1 = 1594324 = 82^2 + 1260^2, so 13 is a term.

%Y Intersection of A000404 and A034472.

%K hard,more,nonn

%O 1,2

%A _Greg Dresden_, Apr 19 2016

%E a(12) = 761 added from the Cunningham Project via _Greg Dresden_, Jul 23 2016

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Last modified January 23 04:16 EST 2020. Contains 331168 sequences. (Running on oeis4.)