# [seqfan] sequence A069987

vincenzo.librandi at tin.it vincenzo.librandi at tin.it
Thu Feb 12 20:33:48 CET 2009

```In the sequence A069987 to include the number 50
n^2+1 = (2, 5, 10, 17,
26, 37, 50, 65, 82, 101,..., )and so on

Regards,
Vincenzo Librandi

%I
A069987
%S A069987
2,5,10,17,26,37,65,82,101,122,145,170,197,226,257,290,362,401,442,485,
%
T A069987
530,577,626,677,730,785,842,901,962,1090,1157,1226,1297,1370,1522,
%U
A069987
1601,1765,1937,2026,2117,2210,2305,2402,2501,2602,2705,2810,2917,3026
%
N A069987 Square-free numbers of form n^2 + 1.
%C A069987 a(n) = A049533
(n)^2+1.
%C A069987 Except for the first term of [A059100], if X=
[A069987], Y=[A000027],
A= [A059100], we have, for all
other terms, Pell's equation: [A069987]^2
- [A059100]*
[A000027]^2=1; (X^2-A*Y^2=1); example: 2^2-3*1^2=1; 5^2-6*2^2=1;
101^2-102*10^2=1; and so on. [From Vincenzo Librandi
(vincenzo.librandi(AT)tin.it),
Feb 11 2009]
%t A069987
Select[ Range[10^4], IntegerQ[ Sqrt[ # - 1]] && Union[ Transpose[
FactorInteger[
# ]] [[2]]] [[ -1]] == 1 &]
%o A069987
(PARI) for(n=1,100,if(issquarefree(n^2+1)==1,print1(n^2+1,",")))
%Y
A069987 Cf. A059591, A002496.
%Y A069987 Cf. A124809, A005117, A002522.
%Y A069987 Sequence in context: A059591 A082607 A002522 this_sequence
A119114 A062493
A056871
%Y A069987 A subsequence of
A000050. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it),
Feb 11 2009]
%Y A069987 Cf. A000027, A059100 [From
Vincenzo Librandi (vincenzo.librandi(AT)tin.it),
Feb 11
2009]
%Y A069987 Adjacent sequences: A069984 A069985 A069986
this_sequence A069988 A069989
A069990
%K A069987 nonn,
new
%O A069987 1,1
%A A069987 Sharon Sela (sharonsela(AT)hotmail.com),
May 01 2002
%E A069987 Edited and extended by Robert G. Wilson v (rgwv
(AT)rgwv.com), Benoit
Cloitre (benoit7848c(AT)orange.