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

2, 7, 12, 17, 22, 27, 32, 37, 42, 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97, 102, 107, 112, 117, 122, 127, 132, 137, 142, 147, 152, 157, 162, 167, 172, 177, 182, 187, 192, 197, 202, 207, 212, 217, 222, 227, 232, 237, 242, 247, 252, 257, 262, 267, 272, 277

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Numbers ending in 2 or 7. - Lekraj Beedassy, Jul 08 2006

For n > 2, also the number of (not necessarily maximal) cliques in the n-gear graph. - Eric W. Weisstein, Nov 29 2017

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

Numbers k such that 2^x + 3^x == 0 mod 31 and 2^x + 3^x == 0 mod 11 with x = 6*k+3. - Pedro Caceres, May 18 2022

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Cino Hilliard, solutions to 3^x + 5^x == 2 mod 11. [broken link]
• Tanya Khovanova, Recursive Sequences.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A001622, A008586, A008587, A016861, A342757.

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

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

Programs

Magma

[5*n+2: n in [0..80]]; // G. C. Greubel, Oct 17 2023

Maple

a[1]:=2:for n from 2 to 100 do a[n]:=a[n-1]+5 od: seq(a[n], n=1..50); # Zerinvary Lajos, Mar 16 2008

Mathematica

Range[2, 500, 5] (* Vladimir Joseph Stephan Orlovsky, May 26 2011 *)
(* Programs from Eric W. Weisstein, Nov 29 2017 *)
5*Range[0, 70] +2
LinearRecurrence[{2, -1}, {7, 12}, {0, 70}]
CoefficientList[Series[(2+3*x)/(1-x)^2, {x,0,70}], x] (* End *)

PARI

a(n)=5*n+2 \\ Charles R Greathouse IV, Jul 10 2016

Sage

[i+2 for i in range(300) if gcd(i,5) == 5] # Zerinvary Lajos, May 20 2009

Formula

a(n) = 10*n - a(n-1) - 1 (with a(0)=2). - Vincenzo Librandi, Nov 20 2010

G.f.: (2+3*x)/(1-x)^2. - Colin Barker, Jan 08 2012

E.g.f.: exp(x)*(2 + 5*x). - Stefano Spezia, Mar 21 2021

Sum_{n>=0} (-1)^n/a(n) = sqrt(2-2/sqrt(5))*Pi/10 + log(phi)/sqrt(5) - log(2)/5, where phi is the golden ratio (A001622). - Amiram Eldar, Apr 15 2023