A088553 -id:A088553 - cp's OEIS frontend

A096724 Duplicate of A088553.

2, 5, 13, 41, 1093, 797161, 21523361, 926510094425921

Offset: 1

dead

A096723 Numbers n such that 3^n has the form 2p-+1 where p is prime.

1, 2, 3, 4, 7, 13, 16, 32, 64, 71, 103, 541, 1091, 1367, 1627, 4177, 9011, 9551, 36913, 43063, 49681, 57917, 483611, 877843, 2215303, 2704981, 3598867

Offset: 1

Lekraj Beedassy, Jul 05 2004

For the corresponding primes p see A088553.

For n > 1, numbers n such that (3^n + (-1)^n)/2 is prime. - Thomas Ordowski, Dec 26 2016

Cf. A028491, A075081, A088553, A093625, A171381.

Select[Range[4200],Or@@PrimeQ[(3^#+{1,-1})/2]&] (* Harvey P. Dale, Mar 05 2013 *)

More terms from Ray Chandler, Jul 09 2004

a(25)-a(27) (from A028491 and A171381) from Tyler Busby, Mar 22 2023

A111009 Starting with the fraction 1/1, the prime numerators of fractions built according to the rule: add top and bottom to get the new bottom, add top and 4 times bottom to get the new top.

Original entry on oeis.org

5, 13, 41, 1093, 797161, 21523361, 926510094425921, 1716841910146256242328924544641, 3754733257489862401973357979128773, 6957596529882152968992225251835887181478451547013

Offset: 1

Cino Hilliard, Oct 02 2005

Or, A046717(n) is prime.

Is this sequence infinite?

Prime Obsession, John Derbyshire, Joseph Henry Press, April 2004, p 16.

Cf. A088553. [From R. J. Mathar, Aug 18 2008]

Select[NestList[(Numerator[#]+4*Denominator[#])/(Numerator[#]+Denominator[#])&,1/1,200]//Numerator,PrimeQ] (* Harvey P. Dale, Jan 04 2024 *)

primenum(n,k,typ) = \ k=mult,typ=1 num,2 denom. ouyput prime num or denom. { local(a,b,x,tmp,v); a=1;b=1; for(x=1,n, tmp=b; b=a+b; a=k*tmp+a; if(typ==1,v=a,v=b); if(isprime(v),print1(v","); ) ); print(); print(a/b+.) }

Given c(0)=1, b(0)=1 then for i=1, 2, .. c(i)/b(i) = (c(i-1)+4*b(i-1)) /(c(i-1) + b(i-1)).

A046717 INTERSECT A000040. [From R. J. Mathar, Aug 18 2008]

Edited by N. J. A. Sloane, Aug 23 2008

cp's OEIS Frontend

A096724 Duplicate of A088553.

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A096723 Numbers n such that 3^n has the form 2p-+1 where p is prime.

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A111009 Starting with the fraction 1/1, the prime numerators of fractions built according to the rule: add top and bottom to get the new bottom, add top and 4 times bottom to get the new top.

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Crossrefs

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