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

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

Author

Zak Seidov, Oct 19 2006

Keywords

• nonn

Comments

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

Links

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

Crossrefs

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

Cf. also A094473.

Programs

Mathematica

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 *)

PARI

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

Formula

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