A392688 Decimal expansion of the addend producing the record value of the Hardy-Littlewood constant from Jacobson (1995).

3, 3, 9, 9, 7, 1, 4, 6, 2, 8, 5, 5, 3, 1, 1, 8, 0, 4, 7

Offset

19,1

Comments

A331940 discusses record addends for the Hardy-Littlewood conjecture. Not part of that sequence, k = 3399714628553118047 as addend in x^2 + x + k is mentioned as one that produces much higher C values than the others listed. Long computation for number of primes up to 10^11 was needed to make first digit past decimal point (C 10.71697) match Hardy-Littlewood constant for that k (C = 10.73416).

Links

Table of n, a(n) for n=19..37.

Michael J. Jacobson, Jr., Computational techniques in quadratic fields, Master's thesis, University of Manitoba, Winnipeg, Manitoba, 1995.

Michael J. Jacobson Jr. and Hugh C. Williams, New Quadratic Polynomials With High Densities Of Prime Values, Math. Comp., 72, 241, 499-519, 2002.

Hermann Stamm-Wilbrandt, computation of numbers of such primes up to 10^x for 0 <= x <= 11.

Example

3399714628553118047

Crossrefs

Cf. A331940.

Sequence in context: A290300 A388529 A201456 * A372267 A347033 A336992

Adjacent sequences: A392685 A392686 A392687 * A392689 A392690 A392691

Keyword

nonn,cons,fini,full

Author

Hermann Stamm-Wilbrandt, Jan 21 2026

Status

approved