login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 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
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
KEYWORD
nonn
AUTHOR
Giovanni Teofilatto, Nov 29 2004
EXTENSIONS
Definition corrected by Robert Israel, Apr 24 2015
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 25 05:01 EST 2024. Contains 370310 sequences. (Running on oeis4.)