A346998 a(n) = A022013(10^n).

88713, 302542763, 46328924003, 1409639621633, 37685138975573, 824339812580723, 16514635234360163, 308319877282402613

Offset: 0

Author

Hugo Pfoertner, Aug 12 2021

Keywords

• nonn
• hard
• more

Comments

The terms are the (10^n)-th initial members of the prime octuplets of the form (p, p+6, p+8, p+14, p+18, 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).

Since this prime constellation leads to the same Hardy-Littlewood constant as for A022011, the expected asymptotic behavior is also the same as in A346996 for large n. See the comment there for more information. Accordingly, the comparison value for a(6) is 1.647755*10^16 and the prediction for a(7) is 3.0824636*10^17.

Links

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

Crossrefs

Cf. A022011, A022012, A022013, A210439, A332493, A346996, A346997.

Extensions

a(7) from Norman Luhn and Hugo Pfoertner, Sep 13 2021