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A164131
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Numbers n such that n^2 ==2 (mod 31).
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0
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8, 23, 39, 54, 70, 85, 101, 116, 132, 147, 163, 178, 194, 209, 225, 240, 256, 271, 287, 302, 318, 333, 349, 364, 380, 395, 411, 426, 442, 457, 473, 488, 504, 519, 535, 550, 566, 581, 597, 612, 628, 643, 659, 674, 690, 705, 721, 736, 752, 767, 783, 798, 814
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Sequences of the type n^2 == 2 (mod m) are basically defined for each m of A057126. See A047341 (m=7), A113804 (m=14), A155449 (m=17), A155450 (m=23), A158803 (m=41) etc. [R. J. Mathar, Aug 26 2009]
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,1,-1)
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FORMULA
| a(n) = a(n-1)+a(n-2)-a(n-3).
a(n) = (31+(-1)^(n-1)+62(n-1))/4.
G.f.: x*(8+15*x+8*x^2)/((1+x)*(x-1)^2). [R. J. Mathar, Aug 26 2009]
a(n)=31*(n-1)-a(n-1), (with a(1)=8) [From Vincenzo Librandi, Nov 30 2010]
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EXAMPLE
| At n= 4, a(4)= (31-1+186)/4=54. At n=5, a(5)=(31+1+248)/4=70.
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MATHEMATICA
| Select[Range[850], Mod[#^2, 31]==2&] (* From Harvey P. Dale, Feb. 4, 2011 *)
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CROSSREFS
| Sequence in context: A003342 A164284 A047719 * A114381 A139433 A178072
Adjacent sequences: A164128 A164129 A164130 * A164132 A164133 A164134
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 11 2009
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EXTENSIONS
| Entries checked by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 26 2009
Deleted an 8 in an A-number of the comment - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 27 2009
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