A029707 Numbers n such that the n-th and the (n+1)-st primes are twin primes.

2, 3, 5, 7, 10, 13, 17, 20, 26, 28, 33, 35, 41, 43, 45, 49, 52, 57, 60, 64, 69, 81, 83, 89, 98, 104, 109, 113, 116, 120, 140, 142, 144, 148, 152, 171, 173, 176, 178, 182, 190, 201, 206, 209, 212, 215, 225, 230, 234, 236, 253, 256, 262, 265, 268, 277

Offset

1,1

Comments

Numbers m such that prime(m)^2 == 1 mod (prime(m) + prime(m + 1)). - Zak Seidov, Sep 18 2013

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..86027

Formula

a(n) = A107770(n) - 1. - Juri-Stepan Gerasimov, Dec 16 2009

Maple

A029707 := proc(n)
    numtheory[pi](A001359(n)) ;
end proc:
seq(A029707(n), n=1..30); # R. J. Mathar, Feb 19 2017

Mathematica

Select[ Range@300, PrimeQ[ Prime@# + 2] &] (* Robert G. Wilson v, Mar 11 2007 *)
Flatten[Position[Flatten[Differences/@Partition[Prime[Range[100]], 2, 1]], 2]](* Harvey P. Dale, Jun 05 2014 *)

Prog

(Sage)
def A029707(n) :
   a = [ ]
   for i in (1..n) :
      if (nth_prime(i+1)-nth_prime(i) == 2) :
         a.append(i)
   return(a)
A029707(277) # Jani Melik, May 15 2014

Crossrefs

Cf. A014574, A027833 (first differences), A007508. Equals PrimePi(A001359) (cf. A000720).

Sequence in context: A364090 A270192 A053034 * A175092 A265250 A090499

Adjacent sequences: A029704 A029705 A029706 * A029708 A029709 A029710

Keyword

nonn

Author

N. J. A. Sloane, Dec 11 1999

Status

approved