

A104375


Smallest prime formed by concatenation of n consecutive cubes, 0 if no such prime exists.


1



0, 827, 0, 2744337540964913, 49135832685980009261, 0, 16194277163870641658137516777216169745931717351217373979, 64348566539203664467267512696859000696787170778887189057, 0
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OFFSET

1,2


COMMENTS

a(n)=0 if n is divisible by 3, as the sum of three consecutive cubes is divisible by 3.
a(22) has 2132 digits, too large for a bfile: it is the concatenation of 99999999999999999999999999999998^3 to 100000000000000000000000000000019^3. (End)


LINKS



EXAMPLE

a(2)=827 because 827 is the smallest prime formed from concatenation of 2 consecutive cubes i.e. 8 and 27.


MAPLE

ccat:= proc(L)
local t, i;
t:= L[1];
for i from 2 to nops(L) do
t:= t*10^(ilog10(L[i])+1)+L[i]
od;
t
end proc:
f:= proc(n) local k, p;
if n mod 3 = 0 then return 0 fi;
for k from floor(n/2)*2+1 by 2 do
p:= ccat([seq((ki)^3, i=n1..0, 1)]);
if isprime(p) then return p fi
od
end proc:
f(1):= 0:


CROSSREFS



KEYWORD

base,nonn


AUTHOR



STATUS

approved



