A100571 Cubes m^3 such that m^3 is the sum of m-1 consecutive primes plus a larger prime.

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

Offset

1,1

Comments

Or, triangular cubic numbers with prime indices. [Comment is not clear to me! - N. J. A. Sloane, Feb 23 2021]

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

Subsequence of A000578.

Sequence in context: A052045 A014187 A050750 * A125084 A052048 A052064

Adjacent sequences: A100568 A100569 A100570 * A100572 A100573 A100574

Keyword

nonn

Author

Giovanni Teofilatto, Nov 29 2004

Extensions

Definition corrected by Robert Israel, Apr 24 2015

Status

approved