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A331941 Hardy-Littlewood constant for the polynomial x^2 + 1. 9
6, 8, 6, 4, 0, 6, 7, 3, 1, 4, 0, 9, 1, 2, 3, 0, 0, 4, 5, 5, 6, 0, 9, 6, 3, 4, 8, 3, 6, 3, 5, 0, 9, 4, 3, 4, 0, 8, 9, 1, 6, 6, 5, 5, 0, 6, 2, 7, 8, 7, 9, 7, 7, 8, 9, 6, 8, 1, 1, 7, 0, 7, 3, 6, 6, 3, 9, 2, 1, 1, 1, 3, 3, 5, 8, 6, 8, 5, 1, 1, 5, 8, 6, 3, 8, 5, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

Henri Cohen, Number Theory, Vol II: Analytic and Modern Tools, Springer (Graduate Texts in Mathematics 240), 2007.

LINKS

Table of n, a(n) for n=0..86.

Karim Belabas, Henri Cohen, Computation of the Hardy-Littlewood constant for quadratic polynomials, PARI/GP script, 2020.

Henri Cohen, High-precision computation of Hardy-Littlewood constants, (1998). [pdf copy, with permission]

Keith Conrad, Hardy-Littlewood Constants, (2003).

FORMULA

C = (1/2)*Product_{p=primes} (1 - Kronecker(-4,p)/(p - 1))

EXAMPLE

0.686406731409123004556096348363509434089166550627879778968117...

PROG

(PARI) See Belabas, Cohen link. Run as HardyLittlewood2(x^2+1)/2 after setting the required precision.

CROSSREFS

Cf. A002496, A005574, A083844, A206709, A221712.

Sequence in context: A331374 A340725 A021597 * A169685 A339606 A200326

Adjacent sequences:  A331938 A331939 A331940 * A331942 A331943 A331944

KEYWORD

nonn,cons

AUTHOR

Hugo Pfoertner, Feb 02 2020

STATUS

approved

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Last modified May 16 14:39 EDT 2021. Contains 343949 sequences. (Running on oeis4.)