The On-Line Encyclopedia of Integer Sequences (OEIS)

A008851 revision #74

A008851

Congruent to 0 or 1 mod 5.

0, 1, 5, 6, 10, 11, 15, 16, 20, 21, 25, 26, 30, 31, 35, 36, 40, 41, 45, 46, 50, 51, 55, 56, 60, 61, 65, 66, 70, 71, 75, 76, 80, 81, 85, 86, 90, 91, 95, 96, 100, 101, 105, 106, 110, 111, 115, 116, 120, 121, 125, 126, 130, 131, 135, 136, 140, 141, 145, 146, 150, 151

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

Numbers k that have the same last digit as k^2.

REFERENCES

L. E. Dickson, History of the Theory of Numbers, I, p. 459.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

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

FORMULA

a(n) = 5*n - a(n-1) - 9, n >= 2. - Vincenzo Librandi, Nov 18 2010 [Corrected for offset by David Lovler, Oct 10 2022]

G.f.: x^2*(1+4*x) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Oct 07 2011

a(n+1) = Sum_{k>=0} A030308(n,k)*A146523(k). - Philippe Deléham, Oct 17 2011

a(n) = floor((5/3)*floor(3*(n-1)/2)). - Clark Kimberling, Jul 04 2012

a(n) = (10*n - 13 - 3*(-1)^n)/4. - Robert Israel, Nov 17 2014 [Corrected by David Lovler, Sep 21 2022]

E.g.f.: 4 + ((10*x - 13)*exp(x) - 3*exp(-x))/4. - David Lovler, Sep 11 2022

Sum_{n>=2} (-1)^n/a(n) = sqrt(1+2/sqrt(5))*Pi/10 + log(phi)/(2*sqrt(5)) + log(5)/4, where phi is the golden ratio (A001622). - Amiram Eldar, Oct 12 2022

MAPLE

a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=a[n-2]+5 od: seq(a[n], n=0..61); # Zerinvary Lajos, Mar 16 2008

MATHEMATICA

Select[Range[0, 151], MemberQ[{0, 1}, Mod[#, 5]] &] (* T. D. Noe, Mar 31 2013 *)

PROG

(Haskell)

a008851 n = a008851_list !! (n-1)

a008851_list = [10*n + m | n <- [0..], m <- [0, 1, 5, 6]]

-- Reinhard Zumkeller, Jul 27 2011

(PARI) a(n) = 5*(n\2)+bitand(n, 1); /* Joerg Arndt, Mar 31 2013 */

(PARI) a(n) = floor((5/3)*floor(3*(n-1)/2)); /* Joerg Arndt, Mar 31 2013 */

(Magma) [n: n in [0..200] | n mod 5 in {0, 1}]; // Vincenzo Librandi, Nov 17 2014