cp's OEIS Frontend

A338850 Continued fraction expansion of the smallest constant 'c' such that the numbers 1+floor(c^(n^1.5)) are distinct primes for all n >= 0.

%I A338850 #12 Nov 17 2020 14:13:29
%S A338850 2,3,1,2,1,2,1,1,1,1,3,1,2,13,6,1,3,5,1,5,1,7,17,1,3,1,11,18,3,1,2,1,
%T A338850 2,1,2,17,15,1,69,3,1,2,1,1,1,1,33,1,3,2,4,17,1,3,2,2,1,2,6,1,11,3,2,
%U A338850 1,1,1,17,1,7,5,2,2,2,84,1,8,3,1,1,22,3698,2,2,1,1,2,1,7,2,1,1,1,1,3,1,5,15,1,3,1,2,1,1,1,1,2,1,16,1,7,2,2,3,1,9
%N A338850 Continued fraction expansion of the smallest constant 'c' such that the numbers 1+floor(c^(n^1.5)) are distinct primes for all n >= 0.
%e A338850 2+1/(3+1/(1+1/(2+1/(1+1/(2+1/(1+1/(1+1/(1+1/(1+1/(3+1/(1+1/(2+1/(13+1/(6]= 590652/260429 = 2.26799626769... The constant 'c' is equal to 2.267996267706724247328553280725371774527042254400818772275…
%o A338850 (PARI)
%o A338850 c(n=40, prec=100)={
%o A338850   my(curprec=default(realprecision));
%o A338850   default(realprecision, max(prec, curprec));
%o A338850   my(a=List([2]), d=1.5, c=2.0, b, p, ok, smpr(b)=my(p=b); while(!isprime(p), p=nextprime(p+1)); return(p); );
%o A338850   for(j=1, n-1,
%o A338850     b=1+floor(c^(j^d));
%o A338850     until(ok,
%o A338850       ok=1;
%o A338850       p=smpr(b);
%o A338850       listput(a,p,j+1);
%o A338850       if(p!=b,
%o A338850          c=(p-1)^(j^(-d));
%o A338850          for(k=1,j-2,
%o A338850              b=1+floor(c^(k^d));
%o A338850              if(b!=a[k+1],
%o A338850                 ok=0;
%o A338850                 j=k;
%o A338850                 break;
%o A338850                );
%o A338850             );
%o A338850         );
%o A338850     );
%o A338850   );
%o A338850   default(realprecision, curprec);
%o A338850   return(c);
%o A338850 };
%o A338850 contfrac(c(50,200),115)
%o A338850 \\ _François Marques_, Nov 17 2020
%Y A338850 Cf. A338613, A338837.
%K A338850 nonn,cofr
%O A338850 1,1
%A A338850 _Bernard Montaron_, Nov 12 2020