A047219 Numbers that are congruent to {1, 3} mod 5.

1, 3, 6, 8, 11, 13, 16, 18, 21, 23, 26, 28, 31, 33, 36, 38, 41, 43, 46, 48, 51, 53, 56, 58, 61, 63, 66, 68, 71, 73, 76, 78, 81, 83, 86, 88, 91, 93, 96, 98, 101, 103, 106, 108, 111, 113, 116, 118, 121, 123, 126, 128, 131, 133, 136, 138, 141, 143, 146, 148

Offset

1,2

Comments

A001844(N)= N^2 + (N+1)^2 is divisible by 5 if and only if N=a(n), n>=1. E.g., n=2: 5|(9 + 16), but 7^2 + 8^2 is not congruent 0 (mod 5). - Wolfdieter Lang, May 09 2012

The number of partitions of 5*(n-1) into at most 2 parts. - Colin Barker, Mar 31 2015

Links

David Lovler, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Formula

a(n) = floor((5*n-3)/2). - Santi Spadaro, Jul 24 2001, corrected by Gary Detlefs, Oct 28 2011

G.f.: x*(1 + 2*x + 2*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Oct 07 2011

a(n) = 2*n + floor((n-1)/2) - 1. - Arkadiusz Wesolowski, Sep 19 2012

Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(1/2 + sqrt(5)/10)*Pi/5 + log(phi)/sqrt(5), where phi is the golden ratio (A001622). - Amiram Eldar, Dec 07 2021

E.g.f.: 2 + ((10*x - 7)*exp(x) - exp(-x))/4. - David Lovler, Aug 23 2022

Mathematica

Flatten[#+{1, 3}&/@(5*Range[0, 30])] (* Harvey P. Dale, Dec 22 2013 *)

Prog

(PARI) a(n)=(5*n-3)\2 \\ Charles R Greathouse IV, Oct 28 2011

Crossrefs

Cf. A000566, A001622, A212160, A212161.

Sequence in context: A360926 A303590 A358844 * A139477 A210570 A224839

Adjacent sequences: A047216 A047217 A047218 * A047220 A047221 A047222

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved