

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
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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] (* JeanFrançois 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



