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%I #23 Nov 01 2013 13:23:45
%S 2,2,76,159,426,406309,4902342,186306983,21138699322,111681723264
%N 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.
%C 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.
%e 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.
%o (PARI)
%o {
%o rec=0;n=2;min=2;b=4;while(1,
%o a=vector(rec+1);
%o for(i=1,rec+1,a[i]=(min+i-1)^(min+i-1));
%o while(1,f=1;
%o for(i=1,rec+1,
%o if(ispseudoprime(n\a[i])==0,
%o f=0;break()));
%o if(f,print(n);rec++;break());
%o n++;if(2>b/n,min++;b=min^min;break())))
%o }
%Y Cf. A000040, A000312.
%K nonn
%O 1,1
%A _James G. Merickel_, Oct 07 2013
%E a(10) added by _James G. Merickel_, Oct 21 2013
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