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A376907 a(n) is the least n-digit cuban prime.

%I A376907 #27 Nov 09 2024 02:37:28
%S A376907 7,19,127,1657,10267,102121,1021417,10052191,100381321,1000556719,
%T A376907 10000510297,100025541019,1000011191887,10000028937841,
%U A376907 100000062634561,1000001305386991,10000001240507791,100000021541868691,1000000084213608427,10000000012591553221,100000000159478313337
%N A376907 a(n) is the least n-digit cuban prime.
%C A376907 a(n) - A011557(n-1) is a multiple of 3.
%H A376907 Robert Israel, <a href="/A376907/b376907.txt">Table of n, a(n) for n = 1..996</a>
%F A376907 Conjecture: a(n+1)/a(n) ~ 10.
%p A376907 nextcuban:= proc(n)
%p A376907   local k,y;
%p A376907   for k from ceil((sqrt(12*n-3)-3)/6) do
%p A376907     y:= (k+1)^3 - k^3;
%p A376907     if isprime(y) then return y fi
%p A376907   od
%p A376907 end proc:
%p A376907 seq(nextcuban(10^i), i = 0 .. 25); # _Robert Israel_, Nov 08 2024
%t A376907 a[n_]:=Module[{k=1},While[!PrimeQ[m=3k^2+3k+1]||IntegerLength[m]<n, k++]; m]; Array[a,15]
%o A376907 (Python)
%o A376907 from itertools import count
%o A376907 from math import isqrt
%o A376907 from sympy import isprime
%o A376907 def A376907(n):
%o A376907     for k in count(isqrt((((a:=10**(n-1))<<2)-1)//12)):
%o A376907         m = 3*k*(k+1)+1
%o A376907         if m >= a and isprime(m):
%o A376907             return m # _Chai Wah Wu_, Oct 13 2024
%Y A376907 Cf. A002407, A003215, A003617, A011557, A111251, A113478, A145203, A376933.
%K A376907 nonn,base
%O A376907 1,1
%A A376907 _Stefano Spezia_, Oct 08 2024