A348053 Alternative version of A332493 (Skewes number for prime n-tuplets).

1369391, 87613571, 1172531, 216646267, 251331775687, 214159878489239, 523250002674163757

Offset: 2

Author

Hugo Pfoertner, Oct 21 2021

Keywords

• nonn
• more
• hard

Comments

In contrast to A332493, in which "latest occurrence" is defined as the largest numerical value of the start of the n-tuplet, the maximum of the position of the occurrence is used here. This distinction is necessary for the first time with the term a(8), because there are 3 possible patterns of 8-tuplets. The 8-tuplet p + [0, 2, 6, 8, 12, 18, 20, 26] leads to A210439(8) = 1203255673037261. Of the two remaining candidates, p + [0, 2, 6, 12, 14, 20, 24, 26] leads to the Hardy-Littlewood prediction being exceeded at the 40634356th 8-tuplet with this pattern, the initial member of which is a(8)=523250002674163757. The other pattern p + [0, 6, 8, 14, 18, 20, 24, 26] leads to the 20316822th 8-tuplet with the beginning A332493(8) = 750247439134737983.

Links

• Tony Forbes and Norman Luhn, Patterns of prime k-tuplets & the Hardy-Littlewood constants.
• Norman Luhn, Database of the smallest prime k-tuplets, compressed files.
• Hugo Pfoertner, Comparison of number of octuplets needed to achieve the H-L prediction, (2021).

Crossrefs

Cf. A210439, A332493.

Extensions

a(8) from Norman Luhn, Sep 11 2021