OFFSET
0,1
COMMENTS
The terms are the (10^n)-th initial members of the prime octuplets of the form (p, p+2, p+6, p+8, p+12, p+18, p+20, p+26). Terms a(5) and a(6) were found using a program provided by Norman Luhn during an effort to find A210439(8) and A332493(8).
Asymptotically for n -> infinity, C_HL*Integral_{x=2..a(n)} 1/log(x)^8 dx = 10^n, where C_HL = 178.261954396542445395360788... is the specific Hardy-Littlewood constant for this prime constellation. The predicted approximate values using this relationship would be a(6) = 1.647755*10^16 and a(7) = 3.0824636*10^17.
LINKS
Norman Luhn, Number of 8-tuplets with initial members < 10^n, (2021).
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Hugo Pfoertner, Aug 11 2021
EXTENSIONS
a(7) from Norman Luhn and Hugo Pfoertner, Sep 14 2021
STATUS
approved