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Search: id:A017173
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| 1, 10, 19, 28, 37, 46, 55, 64, 73, 82, 91, 100, 109, 118, 127, 136, 145, 154, 163, 172, 181, 190, 199, 208, 217, 226, 235, 244, 253, 262, 271, 280, 289, 298, 307, 316, 325, 334, 343, 352, 361, 370, 379, 388, 397, 406, 415, 424, 433, 442, 451, 460, 469, 478
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Also all the numbers with digital root 1; A010888(a(n)) = 1. [From Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jan 12 2009]
A116371(a(n))=A156144(a(n)); positions where records occur in A156144: A156145(n+1)=A156144(a(n)). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 05 2009]
If A=[A147296] 9*n.^2+2*n (n>0, 11, 40, 87,., ,.,); Y=[A010701] 3 (3, 3, 3, ,..,); X=[A017173] 9*n+1 (n>0, 10, 19, 28, ,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 10^2-11*3^2=1; 19^2-40*3^2=1; 28^2-87*3^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 11 2009]
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LINKS
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Tanya Khovanova, Recursive Sequences
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FORMULA
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G.f.: (1+8*x)/(1-x)^2.
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PROGRAM
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(Other) sage: [i+1 for i in range(480) if gcd(i, 9) == 9] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 20 2009]
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CROSSREFS
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Cf. A093644 ((9, 1) Pascal, column m=1).
Cf. A010888. [From Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jan 12 2009]
Cf. A147296, A010701 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 11 2009]
Sequence in context: A098750 A089756 A097153 this_sequence A088410 A126624 A109334
Adjacent sequences: A017170 A017171 A017172 this_sequence A017174 A017175 A017176
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 06 2000
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