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A050798 Numbers n such that m = n^2 + 1 is expressible as the sum of two nonzero squares in exactly two ways. 4
1, 7, 8, 12, 13, 17, 21, 22, 23, 27, 28, 30, 31, 33, 34, 37, 41, 42, 44, 46, 48, 50, 52, 53, 55, 58, 60, 62, 63, 64, 67, 75, 76, 77, 78, 80, 81, 86, 87, 88, 89, 91, 92, 96, 97, 100, 102, 103, 104, 105, 106, 108, 109, 111, 113, 114, 115, 119, 125, 127, 129, 135, 136 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Of course m = n^2 + 1 is the sum of two squares, by definition. Here there should be just one other way to write m as a different sum of two squares.

Let p and q be primes of the form 1+4k. Then n^2+1 must be pq or 2pq. - T. D. Noe, May 27 2008

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

Eric Weisstein, MathWorld: Sum of Squares Function

Index entries for sequences related to sums of squares

EXAMPLE

E.g., 111^2 + 1 = 21^2 + 109^2 only.

MATHEMATICA

ok[1] = True; ok[n_] := Length[ {ToRules[ Reduce[ 1 < x <= y && n^2 + 1 == x^2 + y^2, {x, y}, Integers] ] } ] == 1; Select[ Range[136], ok] (* Jean-Fran├žois Alcover, Feb 16 2012 *)

CROSSREFS

Cf. A000161, A050797, A050796.

Sequence in context: A105740 A050796 A106630 * A260628 A280999 A024706

Adjacent sequences:  A050795 A050796 A050797 * A050799 A050800 A050801

KEYWORD

nonn,nice

AUTHOR

Patrick De Geest, Sep 15 1999

EXTENSIONS

Better definition from T. D. Noe, May 27 2008

STATUS

approved

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Last modified August 3 19:05 EDT 2021. Contains 346441 sequences. (Running on oeis4.)