A134855 -id:A134855 - cp's OEIS frontend

A134854 Least prime of the form 1 + p*2^n, where p is an odd prime.

7, 13, 41, 113, 97, 193, 641, 769, 11777, 13313, 59393, 12289, 40961, 114689, 163841, 2424833, 6946817, 786433, 5767169, 7340033, 23068673, 155189249, 595591169, 1224736769, 167772161, 469762049, 2281701377, 3489660929, 12348030977

Offset: 1

T. D. Noe, Nov 13 2007

nonn

a(n) least prime such that A098006(pi(a(n))) = 2^(n-1). See A134855 for the values of p.

T. D. Noe, Table of n, a(n) for n=1..1000

Table[Select[1+2^n*Prime[Range[2,100]], PrimeQ, 1][[1]], {n,41}]

A245462 a(1)=1, then a(n) is the smallest odd k > floor(a(n-1)/2)+1 such that k*2^n+1 is prime.

Original entry on oeis.org

1, 3, 5, 7, 11, 7, 5, 13, 15, 13, 9, 15, 23, 39, 35, 21, 21, 33, 27, 25, 33, 25, 45, 45, 33, 27, 15, 13, 23, 49, 35, 43, 99, 75, 59, 81, 63, 63, 81, 57, 99, 73, 51, 27, 35, 19, 27, 15, 23, 27, 17, 25, 51, 49, 35, 27, 29, 99, 71, 45

Offset: 1

Pierre CAMI, Jul 22 2014

nonn

A134855(n) = smallest odd k such that k*2^n+1 is prime, the primes are not always in increasing order.
Here the primes k*2^n+1 are always in increasing order.
The ratio sum{k for n=1 to N}/sum{n for n=1 to N} is ~ 2*log(2) as N increases.

Pierre CAMI, Table of n, a(n) for n = 1..6000

Cf. A134855, A245441.

a[n_] := Block[{k = Floor[ a[n - 1]/2] + 2}, If[ EvenQ[k], k++]; While[ !PrimeQ[k*2^n + 1], k += 2]; k]; a[1] = 1; Array[a, 60] (* Robert G. Wilson v, Jul 26 2014 *)

a=[1]; for(n=2, 100, k=floor(a[n-1]/2)+2; if(k%2==0, k++); t=2^n; while(!isprime(k*t+1), k+=2); a=concat(a, k)); a \\ Colin Barker, Jul 23 2014

cp's OEIS Frontend

A134854 Least prime of the form 1 + p*2^n, where p is an odd prime.

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