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

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

Offset

0,1

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

Table of n, a(n) for n=0..7.

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

Crossrefs

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

Sequence in context: A345566 A345821 A031857 * A022548 A022013 A347853

Adjacent sequences: A346995 A346996 A346997 * A346999 A347000 A347001

Keyword

nonn,hard,more

Author

Hugo Pfoertner, Aug 12 2021

Extensions

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

Status

approved