A146763 Rank of terms ending in 0 in A061039.

0, 4, 10, 14, 20, 24, 30, 34, 40, 44, 50, 54, 60, 64, 70, 74, 80, 84, 90, 94, 100, 104, 110, 114, 120, 124, 130, 134, 140, 144, 150, 154, 160, 164, 170, 174, 180, 184, 190, 194, 200, 204, 210, 214, 220, 224, 230, 234, 240, 244, 250, 254, 260, 264, 270, 274

Offset: 0

Author

Paul Curtz, Nov 02 2008

Keywords

• nonn
• base
• easy

Comments

From Paschen spectrum of hydrogen.

Numbers that are congruent to 0 or 4 mod 10. - Philippe Deléham, Oct 18 2011

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A001622, A020714, A030308, A061039.

Programs

Magma

[5*n - (n mod 2): n in [0..60]]; // G. C. Greubel, Mar 10 2022

Mathematica

Select[Range[0, 100], MemberQ[{0,4}, Mod[#, 10]] &] (* K G Teal, Dec 02 2014 *)

Sage

[5*n - (n%2) for n in (0..60)] # G. C. Greubel, Mar 10 2022

Formula

a(n) = 10*n - 6 - a(n-1) (with a(0)=0). - Vincenzo Librandi, Nov 26 2010

a(n) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=4 and b(k) = 5*2^k = A020714(k) for k>0. - Philippe Deléham, Oct 18 2011

From Colin Barker, May 14 2012: (Start)

a(n) = (-1 + (-1)^n + 10*n)/2.

a(n) = a(n-1) + a(n-2) - a(n-3).

G.f.: x*(4+6*x)/((1-x)^2*(1+x)). (End)

E.g.f.: 1/2 (exp(-x) - (1 - 10*x)*exp(x)). - G. C. Greubel, Mar 10 2022

Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(1-2/sqrt(5))*Pi/20 - log(phi)/(4*sqrt(5)) + log(5)/8, where phi is the golden ratio (A001622). - Amiram Eldar, Sep 17 2023