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Search: id:A017281
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| 1, 11, 21, 31, 41, 51, 61, 71, 81, 91, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 201, 211, 221, 231, 241, 251, 261, 271, 281, 291, 301, 311, 321, 331, 341, 351, 361, 371, 381, 391, 401, 411, 421, 431, 441
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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For many of these numbers n (11, 51, 61, 71, 101, 121, 131, 141, 171, 181, etc), (n^2+1)/2 is prime [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Jan 09 2009]
Equals [1, 2, 3,...] convolved with [1, 9, 0, 0, 0,...]. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), May 30 2009]
Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=10, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=2, a(n-1)=-coeff(charpoly(A,x),x^(n-1)). [From Milan R. Janjic (agnus(AT)blic.net), Feb 21 2010]
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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+9*x)/(1-x)^2.
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MAPLE
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with(finance):seq(add(cashflows([3, 3, 4], 0 ), k=1..n)+1, n=0..44); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 21 2008
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MATHEMATICA
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f[n_] := FromDigits[IntegerDigits[n^2, n + 1]]; Array[f, 54] [From Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 14 2009]
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PROGRAM
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(Other) sage: [i+1 for i in range(450) if gcd(i, 10) == 10] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 20 2009]
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CROSSREFS
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Cf. A093645 ((10, 1) Pascal, column m=1).
Subsequence of A034709, together with A017293, A139222, A139245, A017329, A139249, A139264, A139279 and A139280.
Cf. A048161, A154428 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Jan 09 2009]
Cf. A161700, A005408, A016813, A016921, A017533, A158057, A161705, A161709, A161714, A128470. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 17 2009]
Sequence in context: A068633 A123849 A108812 this_sequence A061589 A110402 A081927
Adjacent sequences: A017278 A017279 A017280 this_sequence A017282 A017283 A017284
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KEYWORD
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nonn,easy,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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