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A344125
Decimal expansion of Sum_{i > 0} 1/A001481(i)^4.
2
1, 0, 6, 8, 5, 9, 2, 1, 0, 5, 6, 5, 4, 9, 9, 0, 1, 3, 5, 2, 0, 2, 9, 4, 8, 0, 2, 0, 7, 4, 3, 2, 4, 3, 6, 1, 3, 6, 1, 3, 3, 3, 5, 9, 0, 8, 1, 0, 1, 7
OFFSET
1,3
COMMENTS
This constant can be considered as an analog of zeta(4) (= Pi^4/90 = A013662), where Euler's zeta(4) is over all positive integers, with prime elements in A000040, while this constant is over all positive integers that can be written as the sum of two squares (A001481) with prime elements given in A055025.
FORMULA
Equals Sum_{i > 0} 1/A001481(i)^4.
Equals Product_{i > 0} 1/(1-A055025(i)^-4).
Equals 1/(1-prime(1)^(-4)) * Product_{i>1 and prime(i) == 1 (mod 4)} 1/(1-prime(i)^(-4)) * Product_{i>1 and prime(i) == 3 (mod 4)} 1/(1-prime(i)^(-8)), where prime(n) = A000040(n).
Equals zeta_{2,0} (4) * zeta_{4,1} (4) * zeta_{4,3} (8), where zeta_{2,0} (s) = 2^s/(2^s - 1).
EXAMPLE
1.0685921056549901352029480207432436136133359081017...
CROSSREFS
KEYWORD
nonn,cons,more
AUTHOR
A.H.M. Smeets, May 09 2021
STATUS
approved