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Search: id:A156619
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| A156619 |
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Numbers n such that n^2+1=0 mod (5^2) |
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+0
2
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| 7, 18, 32, 43, 57, 68, 82, 93, 107, 118, 132, 143, 157, 168, 182, 193, 207, 218, 232, 243, 257, 268, 282, 293, 307, 318, 332, 343, 357, 368, 382, 393, 407, 418, 432, 443, 457, 468, 482, 493, 507, 518, 532, 543, 557, 568, 582, 593, 607, 618, 632, 643, 657, 668
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OFFSET
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1,1
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COMMENT
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Also, if a(1)=7, a(2)=18, a(n)=2*a(n-1)-a(n-2)-3 (if n is even); a(n)=2*a(n-1)-a(n-2)+3 (if n is odd); example: a(3)=2*18-7+3=32; a(4)=2*32-18-3=43; a(5)=2*43-32+3=57; a(6)=2*57-43-3=68; the sequence (7,18,32,43,57,68,82,93) repeat to (107,118,..,) (207,218,..,) (307,318,..,) (407,418,...,) and so on
Except for the first term, a(n)=25*n-a(n-1), (with a(1)=18) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 23 2009]
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FORMULA
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n^2+1=0 mod (5^2)
a(n)=a(n-1)+a(n-2)-a(n-3) = 25*n/2-25/4-3*(-1)^n/4. G.f.: x(7+11x+7x^2)/((1+x)(1-x)^2). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 19 2009]
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EXAMPLE
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For n=7, 50=0 mod (25); n=18, 325=0 mod (25); n=468, 219025=0 mod (25).
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CROSSREFS
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Sequence in context: A103571 A103572 A049532 this_sequence A033537 A000566 A133673
Adjacent sequences: A156616 A156617 A156618 this_sequence A156620 A156621 A156622
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KEYWORD
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nonn
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AUTHOR
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Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 11 2009
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