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.

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

1,2

Comments

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.

Links

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

Mathematica

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 *)

Prog

(PFGW & SCRIPT)
SCRIPT
DIM j, -1
DIM n, 0
DIMS t
OPENFILEOUT myf, a(n).txt
LABEL loop1
SET n, n+1
IF n>6000 THEN END
LABEL loop2
SET j, j+2
SETS t, %d, %d\,; n; j
PRP j*2^n+1, t
IF ISPRP THEN GOTO a
GOTO loop2
LABEL a
WRITE myf, t
SET j, j/2
IF j%2==0 THEN SET j, j+1
GOTO loop1
(PARI) 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

Crossrefs

Cf. A134855, A245441.

Sequence in context: A335301 A235379 A174839 * A338842 A022457 A066066

Adjacent sequences: A245459 A245460 A245461 * A245463 A245464 A245465

Keyword

nonn

Author

Pierre CAMI, Jul 22 2014

Status

approved