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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


%S 8,27,64,125,216,343,729,1000,1331,1728,2197,2744,3375,4096,4913,5832,

%T 6859,8000,9261,10648,12167,13824,15625,17576,19683,21952,24389,27000,

%U 29791,32768,35937,39304,42875,46656,50653,54872,59319,64000

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

%C Or, triangular cubic numbers with primes indices.

%C Conjecture: sequence consists of all the cubes > 1 except 8^3=512. - _Giovanni Teofilatto_, Apr 23 2015

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

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

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

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

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

%p kmax:= (pmax-1)/2:

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

%p C:= ListTools:-PartialSums(Primes):

%p A:= NULL:

%p for m from 1 to N-1 do

%p for t from 0 do

%p if t = 0 then q:= (m+1)^3 - C[m]

%p else q:= (m+1)^3 - C[t+m] + C[t]

%p fi;

%p if q <= Primes[t+m] then break fi;

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

%p od

%p od:

%p A; # _Robert Israel_, Apr 24 2015

%K nonn,uned

%O 1,1

%A _Giovanni Teofilatto_, Nov 29 2004

%E Definition corrected by _Robert Israel_, Apr 24 2015

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Last modified April 24 16:26 EDT 2019. Contains 322430 sequences. (Running on oeis4.)