|
|
A127047
|
|
Primes p such that denominator of Sum_{k=1..p-1} 1/k^4 is a fourth power.
|
|
9
|
|
|
2, 3, 5, 7, 11, 13, 17, 19, 29, 31, 53, 67, 71, 73, 97, 101, 103, 107, 109, 127, 131, 197, 199, 211, 223, 227, 229, 233, 293, 367, 373, 379, 383, 389, 397, 401, 439, 443, 449, 457, 461, 463, 557, 563, 569, 571, 577, 877, 881, 883, 967, 971, 977, 983, 991, 997
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
MAPLE
|
S:= 0: R:= NULL: count:= 0:
for k from 1 while count < 100 do
S:= S + 1/k^4;
if isprime(k+1) and surd(denom(S), 4)::integer then R:= R, k+1; count:= count+1 fi
od:
|
|
MATHEMATICA
|
d[n_] := Module[{}, su = 0; a = {}; For[i = 1, i <= n, i++, su = su + 1/ i^4; If[PrimeQ[i + 1], If[IntegerQ[(Denominator[su])^(1/4)], AppendTo[a, i + 1]]]]; a]; d[10000]
Select[Flatten[Position[Denominator[Accumulate[1/Range[1000]^4]], _?(IntegerQ[ Surd[ #, 4]]&)]], PrimeQ] (* Harvey P. Dale, Feb 08 2015 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|