A050798 -id:A050798 - cp's OEIS frontend

A181570 Primes in A050798.

7, 13, 17, 23, 31, 37, 41, 53, 67, 89, 97, 103, 109, 113, 127, 137, 149, 151, 163, 167, 179, 197, 211, 223, 227, 229, 241, 263, 269, 277, 281, 283, 311, 331, 347, 359, 367, 373, 383, 389, 397, 419, 431, 433, 439, 479, 491, 503, 509, 541, 547, 587, 601, 617, 619, 653, 673, 677, 683, 691, 709

Offset: 1

Jonathan Vos Post, Jan 29 2011

Primes p such that p^2 + 1 is expressible as the sum of two nonzero squares in exactly two ways.

Cf. A000040, A000161, A050798.

A050798 INTERSECTION A000040. {p in A000040 such that A000161(p^2 + 1) = 2}.

A050796 Numbers n such that n^2 + 1 is expressible as the sum of two nonzero squares in at least one way (the trivial solution n^2 + 1 = n^2 + 1^2 is not counted).

Original entry on oeis.org

1, 7, 8, 12, 13, 17, 18, 21, 22, 23, 27, 28, 30, 31, 32, 33, 34, 37, 38, 41, 42, 43, 44, 46, 47, 48, 50, 52, 53, 55, 57, 58, 60, 62, 63, 64, 67, 68, 70, 72, 73, 75, 76, 77, 78, 80, 81, 82, 83, 86, 87, 88, 89, 91, 92, 93, 96, 97, 98, 99, 100, 102, 103, 104, 105, 106, 107

Offset: 1

Patrick De Geest, Sep 15 1999

nonn

Analogous solutions exist for the sum of two identical squares z^2 + 1 = 2*r^2 (e.g., 41^2 + 1 = 2*29^2). Values of 'z' are the terms in sequence A002315, values of 'r' are the terms in sequence A001653.
Apart from the first term, numbers n such that (n^2)! == 0 mod (n^2 + 1)^2. - Michel Lagneau, Feb 14 2012
Numbers n such that neither n^2 + 1 nor (n^2 + 1)/2 is prime. - Charles R Greathouse IV, Feb 14 2012

			E.g., 57^2 + 1 = 15^2 + 55^2 = 21^2 + 53^2 = 35^2 + 45^2.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Index entries for sequences related to sums of squares

Cf. A000129, A001653, A002315, A050795, A050798.

t={1}; Do[i=c=2; While[iJayanta Basu, Jun 01 2013 *)

is(n)=!isprime((n^2+1)/if(n%2,2,1)) \\ Charles R Greathouse IV, Feb 14 2012

A050797 Numbers n such that n^2 - 1 is expressible as the sum of two nonzero squares in exactly one way.

Original entry on oeis.org

3, 9, 17, 19, 33, 35, 73, 145, 161, 163, 195, 243, 393, 483, 513, 721, 723, 1153, 1763, 2177, 2305, 2593, 4803, 5185, 5833, 6273, 6963, 7057, 7395, 8713, 9523, 9603, 10083, 12483, 13923, 14113, 15875, 17425, 17673, 19043, 20737

Offset: 1

Patrick De Geest, Sep 15 1999

If the definition were changed from "nonzero squares" to "nonnegative squares", there would be just one additional term, 1. - T. D. Noe, May 27 2008

			E.g. 393^2 - 1 = 28^2 + 392^2 only.

T. D. Noe, Table of n, a(n) for n=1..300
Eric Weisstein, MathWorld: Sum of Squares Function
Index entries for sequences related to sums of squares

Cf. A050798, A050795.

Cf. A000161

twoSquaresQ[ n_] := (r = Reduce [0 < a <= b && n^2 - 1 == a^2 + b^2, {a, b}, Integers]; Head[r] === And); Select[ Range[21000], twoSquaresQ] (* Jean-François Alcover, Oct 10 2011 *)

More terms from James Sellers

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A181570 Primes in A050798.

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A050796 Numbers n such that n^2 + 1 is expressible as the sum of two nonzero squares in at least one way (the trivial solution n^2 + 1 = n^2 + 1^2 is not counted).

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A050797 Numbers n such that n^2 - 1 is expressible as the sum of two nonzero squares in exactly one way.

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