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A134671 Primes of the form 2m*691 - 1.

%I A134671 #26 Feb 16 2025 08:33:07
%S A134671 1381,5527,8291,12437,22111,29021,30403,34549,37313,42841,51133,53897,
%T A134671 58043,62189,70481,92593,96739,105031,120233,134053,145109,167221,
%U A134671 179659,182423,186569,187951,192097,194861,212827,216973,233557,281927
%N A134671 Primes of the form 2m*691 - 1.
%C A134671 Note that all zeros of A046694(n) have the indices equal to the terms of all arithmetic progressions of the type k*p, where primes p belong to a(n). Thus A046694(k*a(n)) = 0 for all integer k > 0.
%H A134671 Amiram Eldar, <a href="/A134671/b134671.txt">Table of n, a(n) for n = 1..10000</a>
%H A134671 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TauFunction.html">Ramanujan's Tau Function</a>.
%e A134671 a(1) = 1381 = 2*691 - 1 is a first prime of the form 2m*691 - 1.
%t A134671 Select[ 2*691*Range[ 1000 ] - 1, PrimeQ[ # ] & ]
%t A134671 Select[Table[1382 n - 1, {n, 0, 300}], PrimeQ] (* _Vincenzo Librandi_, Nov 07 2014 *)
%o A134671 (Magma) [a: n in [0..250] | IsPrime(a) where a is 1382*n-1]; // _Vincenzo Librandi_, Nov 07 2014
%o A134671 (PARI) list(lim)=my(v=List()); forprimestep(p=1381,lim,Mod(-1,1382), listput(v,p)); Vec(v) \\ _Charles R Greathouse IV_, Sep 09 2022
%Y A134671 Cf. A046694 = Ramanujan tau numbers mod 691 = sum of 11th power of divisors mod 691.
%Y A134671 Cf. A121733 = Numbers n such that two consecutive Ramanujan tau numbers are congruent mod 691.
%Y A134671 Cf. A121734 = Ramanujan tau numbers such that A000594[n] == A000594[n+1] mod 691.
%Y A134671 Cf. A121742 = Numbers n such that three consecutive Ramanujan tau numbers are congruent mod 691.
%Y A134671 Cf. A121743 = Values of the Ramanujan tau triples mod 691 such that three consecutive Ramanujan tau numbers are congruent mod 691.
%Y A134671 Cf. A134670 = Least number k such that A046694 has a string of n consecutive zeros starting with A046694(k).
%K A134671 nonn,easy
%O A134671 1,1
%A A134671 _Alexander Adamchuk_, Nov 05 2007