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A100571 Cubes m^3 such that m^3 is the sum of m-1 consecutive primes plus a larger prime. 0
8, 27, 64, 125, 216, 343, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261, 10648, 12167, 13824, 15625, 17576, 19683, 21952, 24389, 27000, 29791, 32768, 35937, 39304, 42875, 46656, 50653, 54872, 59319, 64000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Or, triangular cubic numbers with primes indices.

Conjecture: sequence consists of all the cubes > 1 except 8^3=512. - Giovanni Teofilatto, Apr 23 2015

LINKS

Table of n, a(n) for n=1..38.

EXAMPLE

a(2)=27 because 3^3=3+5+19 and p is 19;

a(3)=64 because 4^3=5+7+11+41 and p is 41;

a(4)=125 because 5^3=5+7+11+13+89 and p is 89.

MAPLE

N:= 100; # to get all terms <= N^3

pmax:= ithprime(N+numtheory:-pi((N+1)^2)):

kmax:= (pmax-1)/2:

Primes:= select(isprime, [2, seq(2*k+1, k=1..kmax)]):

C:= ListTools:-PartialSums(Primes):

A:= NULL:

for m from 1 to N-1 do

for t from 0 do

  if t = 0 then q:= (m+1)^3 - C[m]

  else  q:= (m+1)^3 - C[t+m] + C[t]

  fi;

  if q <= Primes[t+m] then  break fi;

  if isprime(q) then A:= A, (m+1)^3; break fi;

  od

od:

A;  # Robert Israel, Apr 24 2015

CROSSREFS

Sequence in context: A052045 A014187 A050750 * A125084 A052048 A052064

Adjacent sequences:  A100568 A100569 A100570 * A100572 A100573 A100574

KEYWORD

nonn,uned

AUTHOR

Giovanni Teofilatto, Nov 29 2004

EXTENSIONS

Definition corrected by Robert Israel, Apr 24 2015

STATUS

approved

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Last modified March 21 20:35 EDT 2019. Contains 321382 sequences. (Running on oeis4.)