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Search: id:A069987
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| A069987 |
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Square-free numbers of form n^2 + 1. |
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+0
4
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| 2, 5, 10, 17, 26, 37, 65, 82, 101, 122, 145, 170, 197, 226, 257, 290, 362, 401, 442, 485, 530, 577, 626, 677, 730, 785, 842, 901, 962, 1090, 1157, 1226, 1297, 1370, 1522, 1601, 1765, 1937, 2026, 2117, 2210, 2305, 2402, 2501, 2602, 2705, 2810, 2917, 3026
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n) = A049533(n)^2+1.
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]
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MATHEMATICA
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Select[ Range[10^4], IntegerQ[ Sqrt[ # - 1]] && Union[ Transpose[ FactorInteger[ # ]] [[2]]] [[ -1]] == 1 &]
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PROGRAM
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(PARI) for(n=1, 100, if(issquarefree(n^2+1)==1, print1(n^2+1, ", ")))
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CROSSREFS
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Cf. A059591, A002496.
Cf. A124809, A005117, A002522.
Cf. A000027, A059100 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 11 2009]
Sequence in context: A082607 A159547 A002522 this_sequence A119114 A062493 A056871
Adjacent sequences: A069984 A069985 A069986 this_sequence A069988 A069989 A069990
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KEYWORD
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nonn
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AUTHOR
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Sharon Sela (sharonsela(AT)hotmail.com), May 01 2002
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EXTENSIONS
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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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