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A156849
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Numbers n such that n^2 == 2 mod (23^2).
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7
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156, 373, 685, 902, 1214, 1431, 1743, 1960, 2272, 2489, 2801, 3018, 3330, 3547, 3859, 4076, 4388, 4605, 4917, 5134, 5446, 5663, 5975, 6192, 6504, 6721, 7033, 7250, 7562, 7779, 8091, 8308, 8620, 8837, 9149, 9366, 9678, 9895, 10207, 10424
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Numbers n such that n = 153 or 373 mod 529. [Charles R Greathouse IV, Dec 27 2011]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index to sequences with linear recurrences with constant coefficients, signature (1,1,-1).
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FORMULA
| Conjecture: a(n)= +a(n-1) +a(n-2) -a(n-3) = 529*n/2-529/4-95*(-1)^n/4. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 18 2010]
The conjecture is correct. [Charles R Greathouse IV, Dec 27 2011]
G.f.: x*(156+217*x+156*x^2)/(1-x-x^2+x^3). [Colin Barker, Jan 16 2012]
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EXAMPLE
| 156^2-2 == 0 mod (23^2); 373^2-2 == 0 mod (23^2); 685^2-2 == 0 mod (23^2); 10424^2-2 == 0 mod (23^2).
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MATHEMATICA
| With[{c=23^2}, Select[Range[20000], Mod[ #^2-2, c]==0&]] [From Harvey P. Dale (hpd1(AT)nyu.edu), Nov 03 2010]
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PROG
| (PARI) a(n)=529*n/2-529/4-95*(-1)^n/4 \\ Charles R Greathouse IV, Dec 27 2011
(MAGMA) [(1058*n-529-95*(-1)^n)/4: n in [1..50]]; // Vincenzo Librandi, Jan 12 2012
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CROSSREFS
| Cf. A156846, A156845, A156844, A156843, A156842, A156841.
Sequence in context: A166397 A065709 A037983 * A106056 A043356 A038476
Adjacent sequences: A156846 A156847 A156848 * A156850 A156851 A156852
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 17 2009
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EXTENSIONS
| Checked by Joerg Arndt, Jun 16 2010
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