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

1,1

Links

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

Example

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.

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[#]]]] &]

Prog

(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

Crossrefs

Cf. A000578, A048519, A107288.

Sequence in context: A297710 A287945 A238850 * A052014 A236255 A090711

Adjacent sequences: A245061 A245062 A245063 * A245065 A245066 A245067

Keyword

nonn,base

Author

K. D. Bajpai, Jul 11 2014

Status

approved