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

1381, 5527, 8291, 12437, 22111, 29021, 30403, 34549, 37313, 42841, 51133, 53897, 58043, 62189, 70481, 92593, 96739, 105031, 120233, 134053, 145109, 167221, 179659, 182423, 186569, 187951, 192097, 194861, 212827, 216973, 233557, 281927

Offset: 1

Author

Alexander Adamchuk, Nov 05 2007

Keywords

• nonn
• easy

Comments

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.

Examples

			a(1) = 1381 = 2*691 - 1 is a first prime of the form 2m*691 - 1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Ramanujan's Tau Function.

Crossrefs

Cf. A046694 = Ramanujan tau numbers mod 691 = sum of 11th power of divisors mod 691.

Cf. A121733 = Numbers n such that two consecutive Ramanujan tau numbers are congruent mod 691.

Cf. A121734 = Ramanujan tau numbers such that A000594[n] == A000594[n+1] mod 691.

Cf. A121742 = Numbers n such that three consecutive Ramanujan tau numbers are congruent mod 691.

Cf. A121743 = Values of the Ramanujan tau triples mod 691 such that three consecutive Ramanujan tau numbers are congruent mod 691.

Cf. A134670 = Least number k such that A046694 has a string of n consecutive zeros starting with A046694(k).

Programs

Magma

[a: n in [0..250] | IsPrime(a) where a is 1382*n-1]; // Vincenzo Librandi, Nov 07 2014

Mathematica

Select[ 2*691*Range[ 1000 ] - 1, PrimeQ[ # ] & ]
Select[Table[1382 n - 1, {n, 0, 300}], PrimeQ] (* Vincenzo Librandi, Nov 07 2014 *)

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