This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(5) = 12 + 17 + 31 + 33 + 36 = 129 = 2^2 + 5^3.
133 belongs to the sequence because it can be written as 2^3 + 5^3.
sumList[x_List, y_List] := Module[{t = {}}, Do[t = Union[t, x[[i]] + y], {i, Length[x]}]; t]; nn = 10; Select[sumList[Prime[Range[nn]]^3, Prime[Range[nn]]^3], # < Prime[nn]^3 &]
a(4) = 6863 = 19^3 + 2^2.
for n from 1 to 1000 do if (isprime((ithprime(n))^3+4)) then print((ithprime(n))^3+4,4); fi; if (isprime((ithprime(n))^2+8)) then print((ithprime(n))^2+8,8); fi; od;
Join[{17},Select[Prime[Range[300]]^3+4,PrimeQ]] (* Harvey P. Dale, Jul 20 2011 *)
list(lim)=my(v=List([17]), t); lim\=1; forprime(p=3,sqrtnint(lim\1-4,3), if(isprime(t=p^3+4), listput(v, t))); Set(v) \\ Charles R Greathouse IV, Feb 07 2017
a(12) = 1 because 12 = 2^2 + 2^3; a(17) = 1 because 17 = 2^3 + 3^2. a(129) = 2 because 129 = 2^3 + 11^2 = 2^2 + 5^3.
117 belongs to the sequence because it can be written as 5^3 - 2^3.
sumList[x_List, y_List] := (punchline = {}; Do[punchline = Union[punchline, x[[i]] + y], {i, Length[x]}]; punchline); posPart[x_List] := (punchline = {}; Do[If[x[[i]] > 0, punchline = Union[punchline, {x[[i]]}]], {i, Length[x]}]; punchline); posPart[sumList[Prime[Range[10]]^3, - Prime[Range[10]]^3]]
nn=10^5; Union[Reap[Do[n=Prime[i]^3-Prime[j]^3; If[n<=nn, Sow[n]], {i,PrimePi[Sqrt[nn/6]]}, {j,i-1}]][[2,1]]] (* T. D. Noe, Oct 04 2010 *)
With[{upto=20000},Select[Abs[#[[1]]-#[[2]]]&/@Subsets[Prime[ Range[ Sqrt[ upto/6]]]^3,{2}]//Union,#<=upto&]] (* Harvey P. Dale, Dec 10 2017 *)
a(1) = 129 = 2^3+11^2 = 2^2+5^3.
117 and 133 each belong to the (set) sequence because can be written as 117 = 5^3 - 2^3 and 133 = 5^3 + 2^3.
nn=10^6; td=Reap[Do[n=Prime[i]^3-Prime[j]^3; If[n<=nn, Sow[n]], {i,PrimePi[Sqrt[nn/6]]}, {j,i-1}]][[2,1]]; ts=Reap[Do[n=Prime[i]^3+Prime[j]^3; If[n<=nn, Sow[n]], {i,PrimePi[nn^(1/3)]}, {j,i}]][[2,1]]; Union[td,ts] (* T. D. Noe, Oct 04 2010 *)
n = 100; Select[Sort@Flatten@ Table[Prime[i]^3 + (-1)^k Prime[j]^3, {i, n}, {j, i}, {k, 2}], 0 < # < (Prime[n] + 2)^3 - Prime[n]^3 &] (* Ray Chandler, Oct 05 2010 *)
a(1) = 60918125432 = 151^3+246809^2 = 2311^3+220399^2 = 3631^3+114221^2.
53 is in the sequence because 53 = 5^2 + 3^3 + 1 and 3, 5, and 53 are all prime numbers.
isa(n) = {
my(r);
forprime(x = 1, sqrtint(n),
r = n - x ^ 2 - 1;
if( ispower(r, 3, &p) && isprime(p),
return(1)
)
);
return(0)
}
select(isa, primes(1200))
\\ Felix Fröhlich & David A. Corneth & Peter Luschny, Jun 26 2021
from sympy import isprime, primerange
def aupto(lim):
sq = list(p**2 for p in primerange(1, int(lim**(1/2))+2))
cb = list(p**3 for p in primerange(1, int(lim**(1/3))+2))
s3 = set(s for s in (a + b + 1 for a in sq for b in cb) if s <= lim)
return list(filter(isprime, sorted(s3)))
print(aupto(9999)) # Michael S. Branicky, Jun 24 2021
def aList(sup):
P = [p**2 for p in prime_range(1, int(sup**(1/2))+2)]
Q = [(p**3 + 1) for p in prime_range(1, int(sup**(1/3))+2)]
return sorted([a+b for a in P for b in Q if a+b <= sup and is_prime(a+b)])
print(aList(9999)) # Peter Luschny, Jun 25 2021
173 is in the sequence because 173 = 7^2 + 5^3 - 1, and 173, 7, and 5 are all prime.
max = 10^4; Select[Sort[Flatten[Table[Prime[p]^2 + Prime[q]^3 - 1, {p, PrimePi[Sqrt[max]]}, {q, PrimePi[max^(1/3)]}]]], PrimeQ[#] && # < max &] (* Alonso del Arte, Mar 22 2013 *)
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