A047215 Numbers that are congruent to {0, 2} mod 5.

0, 2, 5, 7, 10, 12, 15, 17, 20, 22, 25, 27, 30, 32, 35, 37, 40, 42, 45, 47, 50, 52, 55, 57, 60, 62, 65, 67, 70, 72, 75, 77, 80, 82, 85, 87, 90, 92, 95, 97, 100, 102, 105, 107, 110, 112, 115, 117, 120, 122, 125, 127, 130, 132, 135, 137, 140, 142, 145, 147, 150, 152, 155, 157

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of partitions of 5n into exactly 2 parts. - Colin Barker, Mar 23 2015

Numbers k such that k^2/5 + k*(k + 1)/5 = k*(2*k + 1)/5 is a nonnegative integer. - Bruno Berselli, Feb 14 2017

Links

• David Lovler, Table of n, a(n) for n = 0..1000
• Robbert Fokkink and Gandhar Joshi, Anti-recurrence sequences, arXiv:2506.13337 [math.NT], 2025. See p. 4.
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Different from A038126.

Cf. A001622, A010693, A030308, A084215

Cf. A249547 (partial sums), A010693 (1st differences).

Programs

Magma

[(5*n - (n mod 2))/2: n in [1..100]]; // G. C. Greubel, Jun 23 2024

Mathematica

Table[Floor[5 n/2], {n, 0, 100}] (* or *) LinearRecurrence[{1, 1, -1}, {0, 2, 5},101] (* Vladimir Joseph Stephan Orlovsky, Jan 28 2012 *)

PARI

a(n)=5*n\2 \\ Charles R Greathouse IV, Oct 17 2011

SageMath

[int(5*n//2) for n in range(1,101)] # G. C. Greubel, Jun 23 2024

Formula

a(n) = floor(5*n/2).

From R. J. Mathar, Sep 23 2008: (Start)

G.f.: x*(2 + 3*x)/((1 + x)*(1 - x)^2).

a(n) = 5*n/2 + ((-1)^n-1)/4.

a(n+1) - a(n) = A010693(n+1). (End)

a(n) = 5*n - a(n-1) - 8 with a(1)=0. - Vincenzo Librandi, Aug 05 2010

a(n+1) = Sum_{k>=0} A030308(n,k)*A084215(k+1). - Philippe Deléham, Oct 17 2011

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

Sum_{n>=1} (-1)^(n+1)/a(n) = log(5)/4 - sqrt(5)*log(phi)/10 + sqrt(1-2/sqrt(5))*Pi/10, where phi is the golden ratio (A001622). - Amiram Eldar, Dec 07 2021

E.g.f.: (5*x*exp(x) - sinh(x))/2. - David Lovler, Aug 22 2022