A346997 a(n) = A022012(10^n).

17, 134764997, 9844128377, 345828727877, 9637575539147, 223528482767957, 4652382265065167, 89306626080020957

Offset: 0

Author

Hugo Pfoertner, Aug 11 2021

Keywords

• nonn
• hard
• more

Comments

The terms are the (10^n)-th initial members of the prime octuplets of the form (p, p+2, p+6, p+12, p+14, p+20, p+24, 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 = 475.36521172411318772... is the specific Hardy-Littlewood constant for this prime constellation. The predicted approximate values using this relationship would be a(6) = 4.629899*10^15 and a(7) = 8.9223552*10^16.

Links

• Norman Luhn, Number of 8-tuplets with initial members < 10^n, (2021).

Crossrefs

Cf. A022011, A022012, A022013, A210439, A332493, A346996, A346998.

Extensions

a(7) from Norman Luhn, Sep 13 2021