A337429 -id:A337429 - cp's OEIS frontend

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

Robert G. Wilson v, Aug 25 2002

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

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

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).

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

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

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

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

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

A122118 Least prime factor of 2^n + 5^n.

Original entry on oeis.org

2, 7, 29, 7, 641, 7, 29, 7, 17, 7, 29, 7, 641, 7, 29, 7, 97, 7, 29, 7, 641, 7, 29, 7, 17, 7, 29, 7, 641, 7, 29, 7, 193, 7, 29, 7, 73, 7, 29, 7, 17, 7, 29, 7, 641, 7, 29, 7, 97, 7, 29, 7, 641, 7, 29, 7, 17, 7, 29, 7, 641, 7, 29, 7, 274568286337, 7, 29, 7, 137, 7, 29, 7, 17, 7, 29, 7, 457

Offset: 0

Zak Seidov, Oct 19 2006

nonn

a(n_odd)=7, a(n=2+4k,k=0,1,...)=29, a(64)=274568286337 is unusually large.

Hans Havermann, Table of n, a(n) for n = 0..1023 (terms 0..319 from Antti Karttunen)

Cf. A020639, A074600 (2^n + 5^n), A094475 (primes of form 2^n + 5^n), A122119, A337429.

Cf. also A094473.

Table[FactorInteger[2^n+5^n][[1,1]],{n,0,80}] (* or *) Riffle[Table[ FactorInteger[2^n+5^n][[1,1]],{n,0,80,2}],7] (* The second program is faster *) (* Harvey P. Dale, Mar 02 2015 *)

A122118(n) = { my(k=(2^n+5^n)); forprime(p=if(64==n,274568286337,2),k,if(!(k%p),return(p))); }; \\ Antti Karttunen, Nov 02 2018

a(n) = A020639(A074600(n)). - Antti Karttunen, Nov 02 2018

cp's OEIS Frontend

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

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