

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).


11



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
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OFFSET

1,2


COMMENTS

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


LINKS

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


EXAMPLE

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


MATHEMATICA

t={1}; Do[i=c=2; While[i<n&&c!=0, If[IntegerQ[Sqrt[n^2+1i^2]], c=0; AppendTo[t, n]]; i++], {n, 3, 107}]; t (* Jayanta Basu, Jun 01 2013 *)


PROG

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


CROSSREFS

Cf. A000129, A001653, A002315, A050795, A050798.
Sequence in context: A098731 A294483 A105740 * A106630 A050798 A260628
Adjacent sequences: A050793 A050794 A050795 * A050797 A050798 A050799


KEYWORD

nonn


AUTHOR

Patrick De Geest, Sep 15 1999


STATUS

approved



