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
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