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

1,1

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

Links

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

Example

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

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 *)

Prog

(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
(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

Crossrefs

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

Sequence in context: A082605 A007755 A060611 * A237995 A333081 A178606

Adjacent sequences: A077494 A077495 A077496 * A077498 A077499 A077500

Keyword

nonn

Author

Amarnath Murthy, Nov 07 2002

Extensions

Corrected and extended by Reinhard Zumkeller, Nov 19 2002

More terms from Ray Chandler, Aug 02 2003

Status

approved