|
| |
|
|
A114923
|
|
Primes p such that there exist three primes q, r and s with p^3=q^3+r^3+s^3.
|
|
4
|
|
|
|
709, 1033, 2767, 2791, 2917, 3727, 3769, 5647, 5657, 5737, 7039, 7321, 8089, 8291, 8387, 9433, 9473, 9851, 12073, 12343, 13417, 14083, 14561, 14723, 14831, 14969, 15313, 18127, 19841, 25033, 28081, 28477, 29153, 29179, 32771, 33161, 33199, 33377, 34337, 36713
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
The sets of three primes corresponding to the first seven terms of the sequence are respectively {193,461,631}, {599,691,823}, {103,2179,2213}, {769,1879,2447}, {31,1951,2591}, {1399,1667,3541} and {11,1783,3631}. - Robert G. Wilson v, Jan 09 2006
The sets of three primes corresponding to the next eight terms of the sequence are respectively {2251, 3121, 5171}, {1487, 2731, 5399}, {839, 3691, 5167}, {2099, 2377, 6883}, {3163, 5443, 5843}, {1621, 6323, 6481}, {2357, 4999, 7559} and {1621, 5297, 7589}. - Robert G. Wilson v, Jan 09 2006
The indices of the primes: 127,174,403,406,422,520,525,742,745,754,905,933,1017,1040,1050, ..., . - Robert G. Wilson v, Jan 09 2006
The sets of three primes corresponding to the terms 12073, 12343, 13417, 14083, 14561, 14723, 14831, 14969, 15313, 18127, 19841 and 25033 are respectively {4007, 4327, 11731}, {373, 9209, 10321}, {5099, 7561, 12277}, {4639, 7129, 13259}, {1997, 8599, 13469}, {3881, 6427, 14207}, {6257, 9439, 12959}, {2239, 5189, 14741}, {2269, 2969, 15259}, {2129, 5227, 17971}, {3931, 15263, 16127} and {4093, 19391, 20269}. The indices of the primes: 127, 174, 403, 406, 422, 520, 525, 742, 745, 754, 905, 933, 1017, 1040, 1050, 1168, 1174, 1215, 1446, 1474, 1591, 1661, 1707, 1723, 1738, 1753, 1789, 2077, 2244, 2765. - Farideh Firoozbakht, Jan 27 2006
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
The prime number 3769 is in the sequence because we have 3769^3=11^3+1783^3+3631^3 and three numbers 11, 1783 and 3631 are primes.
|
|
|
MAPLE
|
N:= 20000: # to get all terms <= N
Primes:= select(isprime, [2, seq(i, i=3..N, 2)]):
P2:= {seq(seq(Primes[i]^3 + Primes[j]^3, j=1..i), i=1..nops(Primes))}:
Q:= convert(map(t->-t^3, Primes), set):
filter:= p -> P2 intersect map(`+`, Q, p^3) <> {}:
|
|
|
MATHEMATICA
|
t = {}; Do[ If[p = (Prime[q]^3 + Prime[r]^3 + Prime[s]^3)^(1/3); PrimeQ[p], AppendTo[t, p]; Print[{p, Prime[s], Prime[r], Prime[q]}]], {q, 3, 1059}, {r, q-1}, {s, r-1}]; t (* Robert G. Wilson v, Jan 09 2006 *)
|
|
|
PROG
|
(PARI) is(p)=my(p3=p^3, a3, A, c); if(isprimepower(p3-16)==3, return(1)); forprime(a=sqrtnint(p3\3, 3), sqrtnint(p3-54, 3), a3=a^3; A=p3-a3; forprime(b=3, min(sqrtnint(A, 3), a), if(ispower(A-b^3, 3, &c) && isprime(c), return(isprime(p))))) \\ Charles R Greathouse IV, Nov 24 2017
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
