[seqfan] Re: sequence A069987

[Benoît Jubin]

50 is not square free

On Thu, Feb 12, 2009 at 11:33 AM, vincenzo.librandi at tin.it
<vincenzo.librandi at tin.it> wrote:
> 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.
> fr) and Vladeta Jovovic (vladeta(AT)Eunet.yu),
>               May 04
> 2002
>
>
>
>
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