A187715 a(n) = 5*n - (9 + (-1)^n)/2.

1, 5, 11, 15, 21, 25, 31, 35, 41, 45, 51, 55, 61, 65, 71, 75, 81, 85, 91, 95, 101, 105, 111, 115, 121, 125, 131, 135, 141, 145, 151, 155, 161, 165, 171, 175, 181, 185, 191, 195, 201, 205, 211, 215, 221, 225

Offset: 1

Author

Vincenzo Librandi, Mar 13 2011

Keywords

• nonn
• easy

Comments

Numbers congruent to {1,5} mod 10. - Bruno Berselli, Mar 31 2012

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A001622, A010711 (first differences), A017281, A017329.

Programs

GAP

Filtered([1..250],n-> n mod 10 =1 or n mod 10 = 5); # Muniru A Asiru, Nov 25 2018

Magma

[5*n -(9+(-1)^n)/2: n in [1..60]];

Maple

[5*n-(9+(-1)^n)/2$n=1..50]; # Muniru A Asiru, Nov 25 2018

Mathematica

nxt[{n_,a_}]:={n+1,If[EvenQ[n+1],a+4,a+6]}; Transpose[NestList[nxt,{1,1},50]][[2]] (* Harvey P. Dale, Feb 16 2013 *)
Table[BitOr[5*n, 1], {n, 0, 50}] (* Jon Maiga, Nov 24 2018 *)

PARI

vector(50, n, (10*n -9-(-1)^n)/2) \\ G. C. Greubel, Dec 04 2018

Python

for n in range(1,60): print(int(5*n - (9 + (-1)**n)/2), end=', ') # Stefano Spezia, Nov 30 2018

Sage

[(10*n -9-(-1)^n)/2 for n in (1..50)] # G. C. Greubel, Dec 04 2018

Formula

a(n) = a(n-1) + 4 if n is even, a(n) = a(n-1) + 6 if n is odd.

a(n) = 2*a(n-1) - a(n-2) - 2*(-1)^n.

From R. J. Mathar, Mar 15 2011: (Start)

G.f.: x*(1 + 4*x + 5*x^2)/( (1+x)*(1-x)^2 ).

Bisections: a(2*n+1) = A017281(n), a(2*n) = A017329(n-1). (End)

a(n) = 5*(n-1) bitwise-OR 1. - Jon Maiga, Nov 24 2018

E.g.f.: ((10*x-9)*exp(x) - exp(-x) + 10)/2. - G. C. Greubel, Dec 04 2018

Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(5+2*sqrt(5))*Pi/20 + 3*log(phi)/(4*sqrt(5)) + log(5)/8, where phi is the golden ratio (A001622). - Amiram Eldar, Apr 15 2023

Extensions

Definition rewritten by R. J. Mathar, Mar 15 2011