|
|
A077497
|
|
Primes of the form 2^r*5^s + 1.
|
|
10
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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;
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|