A077497 Primes of the form 2^r*5^s + 1.

2, 3, 5, 11, 17, 41, 101, 251, 257, 401, 641, 1601, 4001, 16001, 25601, 40961, 62501, 65537, 160001, 163841, 16384001, 26214401, 40960001, 62500001, 104857601, 167772161, 256000001, 409600001, 655360001, 2441406251, 2500000001, 4194304001, 10485760001

Offset: 1

Author

Amarnath Murthy, Nov 07 2002

Keywords

• nonn

Comments

These are also the prime numbers p for which there is an integer solution x to the equation p*x = p*10^p + x, or equivalently, the prime numbers p for which (p*10^p)/(p-1) is an integer. - Vicente Izquierdo Gomez, Feb 20 2013

For n > 2, all terms are congruent to 5 (mod 6). - Muniru A Asiru, Sep 03 2017

Examples

			101 is in the sequence, since 101 = 2^2*5^2 + 1 and 101 is prime.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..3150

Crossrefs

Cf. A005109, A077497, A077498, A077500, A003592, A077313, A019434.

Programs

GAP

K:=10^7;; # to get all terms <= K.
A:=Filtered(Filtered([1..K],i-> i mod 6=5),IsPrime);;
B:=List(A,i->Factors(i-1));;
C:=[];;  for i in B do if Elements(i)=[2] or Elements(i)=[2,5]  then Add(C,Position(B,i)); fi; od;
A077497:=Concatenation([2,3],List(C,i->A[i])); # Muniru A Asiru, Sep 03 2017

Mathematica

Do[p=Prime[k];s=FindInstance[p x == p 10^p+x,x,Integers];If[s!={},Print[p]],{k,10000}] (* Vicente Izquierdo Gomez, Feb 20 2013 *)

PARI

list(lim)=my(v=List(),t);for(r=0,log(lim)\log(5),t=5^r;while(t<=lim,if(isprime(t+1),listput(v,t+1)); t<<=1)); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jan 29 2013

Extensions

Corrected and extended by Reinhard Zumkeller, Nov 19 2002

More terms from Ray Chandler, Aug 02 2003