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
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
KEYWORD
nonn
AUTHOR
Giovanni Teofilatto, Nov 29 2004
EXTENSIONS
Definition corrected by Robert Israel, Apr 24 2015
STATUS
approved