A230054 - OEIS

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A230054

The smallest integer a(n) = A producing primes for the first n values greater than 1 of floor((k^k)/A), k drawn from the positive integers.

2, 2, 76, 159, 426, 406309, 4902342, 186306983, 21138699322, 111681723264

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OFFSET

1,1

COMMENTS

For the 10 values shown, the first value of k meeting the criterion are 2, 2, 4, 5, 5, 7, 8, 9, 11, and 11.

LINKS

Table of n, a(n) for n=1..10.

EXAMPLE

Last two in detail: (10^10)/21138699322 < 2, while floor((k^k)/21138699322) for k=11 to 19 evaluates as 13, 421, 14327, 525671, 20715271, 872652749, 39133924433, 1861344800639 and 93592307905211, all prime. 21138699322 is the smallest value that gives 9 primes in succession this way, and is therefore the value of a(9). For a(10)=11681723264, the minimum 2 is the value of the first prime (still with k=11), and 79, 2711, 99497, 3920909, 165172451, 7407123007, 352308389639, 17714802367291 and 938896687259483 follow for k=12 to 20.

PROG

(PARI)

{

rec=0; n=2; min=2; b=4; while(1,

a=vector(rec+1);

for(i=1, rec+1, a[i]=(min+i-1)^(min+i-1));

while(1, f=1;

for(i=1, rec+1,

if(ispseudoprime(n\a[i])==0,

f=0; break()));

if(f, print(n); rec++; break());

n++; if(2>b/n, min++; b=min^min; break())))