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 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 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

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Last modified June 3 14:25 EDT 2023. Contains 363116 sequences. (Running on oeis4.)