A225584 Primes in the chain of repeated application of x->2*x+3, starting at x=23.

23, 101, 829, 6653, 13309, 6815741, 436207613, 13958643709, 27917287421, 468374361246531581, 3746994889972252669, 959230691832896684029, 16093220510709943573688614909

Offset: 1

Author

Vincenzo Librandi, May 14 2013

Keywords

• nonn
• easy

Comments

Primes in A156202.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..31

Crossrefs

Primes of the form k*2^m-3: A050415 (k=1), A173769 (k=5), A225582 (k=7), A225583 (k=11), this sequence (k=13); A172156 (k=100), A163589 (k=715).

Numbers of the form 13*2^m-3: A156202.

Programs

Magma

x:=23; a:=[n eq 1 select x else 2*Self(n-1)+3: n in [1..200]]; [a[i]: i in [1..#a] | IsPrime(a[i])];

Magma

[a: n in [0..150] | IsPrime(a) where a is 13*2^n-3];

Mathematica

Select[NestList[2 # + 3 &, 23, 30], PrimeQ] (* or *) Select[Table[13 2^(n+1) - 3, {n, 0, 150}], PrimeQ]