A127047 Primes p such that denominator of Sum_{k=1..p-1} 1/k^4 is a fourth power.

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

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..665 from Robert Israel)

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:
R; # Robert Israel, Oct 25 2019

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

Cf. A061002, A034602, A127029, A127042, A127046.

Sequence in context: A348358 A171821 A004051 * A119615 A061771 A124589

Adjacent sequences: A127044 A127045 A127046 * A127048 A127049 A127050

Keyword

nonn,look

Author

Artur Jasinski, Jan 03 2007

Status

approved