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Cyclops primes that become a cube when the middle "0" is removed.
1

%I #33 Dec 25 2019 04:44:34

%S 68059,1170649,4560533,7530571,136501919,158103251,173703979,

%T 212503933,226605187,356101289,362604691,382702753,439806977,

%U 518905117,811802737,954403993,19484041249,19956016979,22635071297,24658046551,27263097773,34635012697,35326042667,37166072149,39668022287,41499095543,44839062449

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

%H 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 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 136501919 is a term because 13651919 is 239^3.

%p count:= 0: Res:= NULL:

%p for d from 2 to 6 do

%p for n from ceil(10^((2*d-1)/3)) to floor((10^(2*d)-1)^(1/3)) do

%p L:=convert(n^3,base,10);

%p if member(0,L) then next fi;

%p a:= n^3 mod 10^d;

%p p:= 10*(n^3-a)+a;

%p if isprime(p) then

%p count:= count+1; Res:= Res, p;

%p fi

%p od od:

%p Res; # _Robert Israel_, Dec 24 2019

%o (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 Cf. A329737, A134809, A016755.

%K nonn,base,easy

%O 1,1

%A _Rodolfo Ruiz-Huidobro_, Dec 14 2019