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A330414 Cyclops primes that become a cube when the middle "0" is removed.

%I A330414 #33 Dec 25 2019 04:44:34
%S A330414 68059,1170649,4560533,7530571,136501919,158103251,173703979,
%T A330414 212503933,226605187,356101289,362604691,382702753,439806977,
%U A330414 518905117,811802737,954403993,19484041249,19956016979,22635071297,24658046551,27263097773,34635012697,35326042667,37166072149,39668022287,41499095543,44839062449
%N A330414 Cyclops primes that become a cube when the middle "0" is removed.
%H A330414 Robert Israel, <a href="/A330414/b330414.txt">Table of n, a(n) for n = 1..10000</a> (first 60 terms from Rodolfo Ruiz-Huidobro)
%e A330414 a(1) = 68059 because 6859 = 19^3 is the first cube that results from the removal of the 0 digit from a cyclops prime.
%e A330414 136501919 is a term because 13651919 is 239^3.
%p A330414 count:= 0: Res:= NULL:
%p A330414 for d from 2 to 6 do
%p A330414   for n from ceil(10^((2*d-1)/3)) to floor((10^(2*d)-1)^(1/3)) do
%p A330414     L:=convert(n^3,base,10);
%p A330414     if member(0,L) then next fi;
%p A330414     a:= n^3 mod 10^d;
%p A330414     p:= 10*(n^3-a)+a;
%p A330414     if isprime(p) then
%p A330414       count:= count+1; Res:= Res, p;
%p A330414     fi
%p A330414 od od:
%p A330414 Res; # _Robert Israel_, Dec 24 2019
%o A330414 (PARI) seq(n)={my(i=0, L=List()); while(#L<n, i++; my(v=digits(i^3), k=#v\2); if(#v==2*k && !#select(t->t==0,v), my(m=fromdigits(concat([v[1..k], 0, v[k+1..#v]]))); if(isprime(m), listput(L,m)))); Vec(L)} \\ _Andrew Howroyd_, Dec 20 2019
%Y A330414 Cf. A329737, A134809, A016755.
%K A330414 nonn,base,easy
%O A330414 1,1
%A A330414 _Rodolfo Ruiz-Huidobro_, Dec 14 2019