A339458 - OEIS

A339458

Continued fraction expansion of the smallest constant d such that the numbers floor(2^(n^d)) are distinct primes for all n >= 1.

1, 1, 1, 63, 7, 3, 2, 2, 1, 1, 1, 250, 2, 1, 2, 1, 2, 3, 1, 4, 1, 1, 3, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 6, 7, 1, 1, 1, 6, 1, 1, 9, 9, 2, 1, 6, 2, 5, 1, 25, 1, 1, 1, 2, 18, 1, 3, 5, 1, 1, 5, 1, 3, 1, 1, 4, 1, 1, 3, 2, 2, 3, 40, 2, 3, 8, 2, 2, 25, 1, 5, 2, 1, 1, 3, 2, 2, 1, 10, 1, 1, 2, 1, 2, 1, 1, 2, 1, 3, 2, 420, 2, 2, 1

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OFFSET

1,4

LINKS

Table of n, a(n) for n=1..106.

EXAMPLE

1+1/(1+1/(1+1/(63+1/(7+1/(3+1/(2+1/(2+1/(1+1/(1+1/(1+1/(250] = 22739482/15120055 = 1.503928524069522...

The constant is equal to d=1.503928524069520633527689067897583199190738849581138429002999...

PROG

(PARI) A339458(n=63, prec=200)={

my(curprec=default(realprecision));

default(realprecision, max(prec, curprec));

my(a=List([2]), d=1.0, c=2.0, b, p, ok, smpr(b)=my(p=b); while(!isprime(p), p=nextprime(p+1)); return(p); );

for(j=1, n-1,

b=floor(c^(j^d));

until(ok,

p=smpr(b);

ok = 1;

listput(a, p, j);

if(p!=b,

d=log(log(p)/log(c))/log(j);

for(k=1, j-2,

b=floor(c^(k^d));

if(b!=a[k],

ok=0;

j=k;

break;

);

default(realprecision, curprec);

return(contfrac(d));

} \\ François Marques, Dec 08 2020

CROSSREFS

Cf. A339459, A339457, A338613, A338837, A338850.

Sequence in context: A255915 A351341 A234692 * A084507 A202157 A145585

Adjacent sequences: A339455 A339456 A339457 * A339459 A339460 A339461

KEYWORD

nonn,cofr

AUTHOR

Bernard Montaron, Dec 06 2020

STATUS

approved