A104375 Smallest prime formed by concatenation of n consecutive cubes, 0 if no such prime exists.

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

Offset

1,2

Comments

From Robert Israel, Feb 20 2020: (Start)

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 b-file: it is the concatenation of 99999999999999999999999999999998^3 to 100000000000000000000000000000019^3. (End)

Links

Robert Israel, Table of n, a(n) for n = 1..21

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((k-i)^3, i=n-1..0, -1)]);
    if isprime(p) then return p fi
  od
end proc:
f(1):= 0:
map(f, [$1..10]); # Robert Israel, Feb 20 2020

Crossrefs

Sequence in context: A237062 A251616 A251611 * A066946 A143799 A046496

Adjacent sequences: A104372 A104373 A104374 * A104376 A104377 A104378

Keyword

base,nonn

Author

Shyam Sunder Gupta, Apr 17 2005

Status

approved