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Search: id:A047522
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| A047522 |
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Numbers that are congruent to {1, 7} mod 8. |
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+0
4
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| 1, 7, 9, 15, 17, 23, 25, 31, 33, 39, 41, 47, 49, 55, 57, 63, 65, 71, 73, 79, 81, 87, 89, 95, 97, 103, 105, 111, 113, 119, 121, 127, 129, 135, 137, 143, 145, 151, 153, 159, 161, 167, 169, 175, 177, 183, 185, 191, 193, 199
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Also n such that Kronecker(2,n)==mu(gcd(2,n)). - Jon Perry (perry(AT)globalnet.co.uk) and T. D. Noe (noe(AT)sspectra.com), Jun 13 2003
n such that x^2 == 2 (mod n) has a solution. The primes are given in sequence A001132. - T. D. Noe (noe(AT)sspectra.com), Jun 13 2003
As indicated in the formula, a(n) is related to the even triangular numbers. - Frederick Magata (frederick.magata(AT)t-online.de), Jun 17 2004
Except for the first term of [A047522] and the first term of [A074378], if X=[A047522], Y=[A010709], A=[A074378], we have, for all other terms, Pell's equation X^2-A*Y^2=1. Example 9^2-5*4^2=1; 15^2-14*4^2=1; 17^2-18*4^2=1 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 14 2009]
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REFERENCES
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L. B. W. Jolley, "Summation of Series", Dover Publications, p. 16.
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FORMULA
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a(n)=sqrt(8*A014494(n)+1)=sqrt(16*ceiling[n/2]*(2*n+1)+1)=sqrt(8*A056575(n)-8*(2n+1)*(-1)^n+1). - Frederick Magata (frederick.magata(AT)t-online.de), Jun 17 2004
1 - 1/7 + 1/9 - 1/15 + 1/17... = (Pi/8)*(1 + sqrt(2)). [Jolley] - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 16 2006
a(n)= 4n-2+(-1)^n = a(n-2)+8. G.f.: x(1+6x+x^2)/((1+x)(1-x)^2). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 19 2009]
Except for the first term, a(n)=8*n-a(n-1), (with a(1)=7) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 18 2009]
a(n)=8*n-a(n-1)-8 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 24 2009]
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EXAMPLE
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n=2, a(2)=8*2-7=9; n=3, a(3)=8*3-9=15; n=4, a(4)=8*4-15=17 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 18 2009]
For n=2, a(2)=8*2-1-8=7; n=3, a(3)=8*3-7-8=9; n=4, a(4)=8*4-9-8=15 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 24 2009]
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MATHEMATICA
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Select[Range[1, 191, 2], JacobiSymbol[2, # ]==1&]
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CROSSREFS
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Cf. A001132.
Cf. A014494, A056575.
Cf. A010709, A074378 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 14 2009]
Sequence in context: A020939 A073457 A067873 this_sequence A112072 A024902 A111312
Adjacent sequences: A047519 A047520 A047521 this_sequence A047523 A047524 A047525
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KEYWORD
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nonn,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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