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A016873 a(n) = 5n + 2. 29

%I

%S 2,7,12,17,22,27,32,37,42,47,52,57,62,67,72,77,82,87,92,97,102,107,

%T 112,117,122,127,132,137,142,147,152,157,162,167,172,177,182,187,192,

%U 197,202,207,212,217,222,227,232,237,242,247,252,257,262,267,272,277

%N a(n) = 5n + 2.

%C Also solutions to 3^x + 5^x == 1 mod 11. - _Cino Hilliard_, May 18 2003

%C Numbers ending in 2 or 7. - _Lekraj Beedassy_, Jul 08 2006

%C For n > 2, also the number of (not necessarily maximum) cliques in the n-gear graph. - _Eric W. Weisstein_, Nov 29 2017

%C Also, positive integers k such that 10*k+5 is equal to the product of two integers ending with 5. Proof: if 10*k+5 = (10*a+5) * (10*b+5), then k = 10*a*b + 5*(a+b) + 2 = 5 * (a + b + 2*a*b) + 2, of the form 5m + 2. So, 262 is a term because 2625 = 35 * 75. - _Bernard Schott_, May 15 2019

%H Cino Hilliard, <a href="http://groups.msn.com/BC2LCC/3x5x211k.msnw">solutions to 3^x + 5^x == 2 mod 11</a> [broken link]

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = 10*n - a(n-1) - 1 (with a(0)=2). - _Vincenzo Librandi_, Nov 20 2010

%F G.f.: (2+3*x)/(1-x)^2. - _Colin Barker_, Jan 08 2012

%p a[1]:=2:for n from 2 to 100 do a[n]:=a[n-1]+5 od: seq(a[n], n=1..47); # _Zerinvary Lajos_, Mar 16 2008

%t Range[2, 500, 5] (* _Vladimir Joseph Stephan Orlovsky_, May 26 2011 *)

%t Table[5 n + 2, {n, 0, 20}] (* _Eric W. Weisstein_, Nov 29 2017 *)

%t 5 Range[0, 20] + 2 (* _Eric W. Weisstein_, Nov 29 2017 *)

%t LinearRecurrence[{2, -1}, {7, 12}, {0, 20}] (* _Eric W. Weisstein_, Nov 29 2017 *)

%t CoefficientList[Series[(2 + 3 x)/(-1 + x)^2, {x, 0, 20}], x] (* _Eric W. Weisstein_, Nov 29 2017 *)

%o (Sage) [i+2 for i in range(235) if gcd(i,5) == 5] # _Zerinvary Lajos_, May 20 2009

%o (PARI) a(n)=5*n+2 \\ _Charles R Greathouse IV_, Jul 10 2016

%Y Cf. A008586, A008587, A016861.

%Y Cf. A053742 (product of two integers ending with 5).

%Y Cf. A324298 (similar with product of two integers ending with 6).

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_

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Last modified November 12 17:06 EST 2019. Contains 329058 sequences. (Running on oeis4.)