A074600 a(n) = 2^n + 5^n.

2, 7, 29, 133, 641, 3157, 15689, 78253, 390881, 1953637, 9766649, 48830173, 244144721, 1220711317, 6103532009, 30517610893, 152587956161, 762939584197, 3814697527769, 19073486852413, 95367432689201, 476837160300277

Offset: 0

Author

Robert G. Wilson v, Aug 25 2002

Keywords

• easy
• nonn

Comments

Digital root of a(n) is A010697(n). - Peter M. Chema, Oct 24 2016

References

• Miller, Steven J., ed. Benford's Law: Theory and Applications. Princeton University Press, 2015. See page 14.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• D. Suprijanto, I. W. Suwarno, Observation on Sums of Powers of Integers Divisible by 3k-1, Applied Mathematical Sciences, Vol. 8, 2014, no. 45, pp. 2211-2217.
• Index entries for linear recurrences with constant coefficients, signature (7,-10).

Crossrefs

Cf. A000051, A034472, A052539, A034474, A062394, A034491, A062395, A062396, A007689, A063376, A063481, A074601-A074624, A010697, A094475, A337429.

Programs

Magma

[2^n + 5^n: n in [0..35]]; // Vincenzo Librandi, Apr 30 2011

Mathematica

Table[2^n + 5^n, {n, 0, 25}]
LinearRecurrence[{7,-10},{2,7},30] (* Harvey P. Dale, May 09 2019 *)

PARI

a(n)=2^n+5^n \\ Charles R Greathouse IV, Sep 24 2015

Formula

a(n) = 5*a(n-1)-3*2^(n-1) = 7*a(n-1)- 10*a(n-2). [Corrected by Zak Seidov, Oct 24 2009]

G.f.: 1/(1-2*x)+1/(1-5*x). E.g.f.: e^(2*x)+e^(5*x). - Mohammad K. Azarian, Jan 02 2009