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a(n) = A022013(10^n).
5

%I #16 Aug 23 2022 08:45:19

%S 88713,302542763,46328924003,1409639621633,37685138975573,

%T 824339812580723,16514635234360163,308319877282402613

%N a(n) = A022013(10^n).

%C 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).

%C 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.

%H Norman Luhn, <a href="https://pzktupel.de/counting/PI_08.php">Number of 8-tuplets with initial members < 10^n</a>, (2021).

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

%K nonn,hard,more

%O 0,1

%A _Hugo Pfoertner_, Aug 12 2021

%E a(7) from _Norman Luhn_ and _Hugo Pfoertner_, Sep 13 2021