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A047219 Numbers that are congruent to {1, 3} mod 5. 33
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..60.

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

Row sums of triangle A131900. - Gary W. Adamson, Jul 25 2007

a(n) = 5*n-a(n-1)-6 (with a(1)=1). - Vincenzo Librandi, Aug 05 2010

a(n) = (1/4)*[ -7-(-1)^n+10*n], with n>=1. - Paolo P. Lava, Sep 03 2010

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

MATHEMATICA

Select[Range[0, 200], MemberQ[{1, 3}, Mod[#, 5]] &] (* Vladimir Joseph Stephan Orlovsky, Feb 12 2012 *)

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, A131900, A212160, A212161.

Sequence in context: A190229 A190085 A303590 * A139477 A210570 A224839

Adjacent sequences:  A047216 A047217 A047218 * A047220 A047221 A047222

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 15 11:18 EST 2019. Contains 329144 sequences. (Running on oeis4.)