Search: id:A069987
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%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 Cf. A000027, A059100 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Feb 11 2009]
%Y A069987 Sequence in context: A082607 A159547 A002522 this_sequence A119114 A062493 
               A056871
%Y A069987 Adjacent sequences: A069984 A069985 A069986 this_sequence A069988 A069989 
               A069990
%K A069987 nonn
%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.fr) and Vladeta Jovovic (vladeta(AT)eunet.rs), 
               May 04 2002

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