A245064 Primes p such that p minus its digit sum is a perfect cube.

2, 3, 5, 7, 31, 37, 223, 227, 229, 743, 1741, 1747, 3391, 5851, 5857, 9281, 9283, 13841, 19709, 27011, 27017, 35963, 35969, 46681, 46687, 59341, 74101, 91141, 110603, 110609, 132679, 373273, 474581, 474583, 729023, 804383, 1061227, 1259743, 1259749, 1481573, 2000393

Offset: 1

Author

K. D. Bajpai, Jul 11 2014

Keywords

• nonn
• base

Examples

			37 is in the sequence because it is prime. Also, 37 - (3 + 7 ) = 27 = 3^3: a perfect cube.
743 is in the sequence because it is prime. Also, 743 - (7 + 4 + 3) = 729 = 9^3: a perfect cube.
		

Links

• K. D. Bajpai and Jens Kruse Andersen, Table of n, a(n) for n = 1..10000 (first 274 terms from K. D. Bajpai)

Crossrefs

Cf. A000578, A048519, A107288.

Programs

Maple

dmax:= 9; # to get all entries < 10^dmax
cmax:= floor(10^(dmax/3));
count:= 0;
for m from 0 to cmax do
   for p from m^3 to m^3 + 9*dmax do
      if p - convert(convert(p,base,10),`+`) = m^3 and isprime(p) then
         count:= count+1;
         A[count]:= p;
      fi
   od
od;
{seq(A[i],i=1..count)}; # Robert Israel, Jul 15 2014

Mathematica

Select[Prime[Range[200000]], IntegerQ[CubeRoot[# - Apply[Plus, IntegerDigits[#]]]] &]

PARI

digsum(n) = my(d=eval(Vec(Str(n)))); sum(i=1, #d, d[i])
s=[]; forprime(p=2, 2002000, if(ispower(p-digsum(p), 3), s=concat(s, p))); s \\ Colin Barker, Jul 15 2014