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A245064 Primes p such that p minus its digit sum is a perfect cube. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 20 04:21 EST 2019. Contains 319323 sequences. (Running on oeis4.)