A354604 Midpoints of record gaps between primes: a(n) = (A000101(n) + A002386(n))/2 for n > 1.

4, 9, 26, 93, 120, 532, 897, 1140, 1344, 9569, 15705, 19635, 31433, 155964, 360701, 370317, 492170, 1349592, 1357267, 2010807, 4652430, 17051797, 20831428, 47326803, 122164858, 189695776, 191912907, 387096258, 436273150, 1294268635, 1453168287, 2300942709, 3842610941, 4302407536, 10726904850, 20678048489, 22367085156, 25056082315, 42652618575

Offset: 2

Author

Donghwi Park, Jul 08 2022

Keywords

• nonn

Comments

In the displayed portion of the sequence, the only numbers of least prime signature (A025487) are 4 and 120. This is noteworthy because numbers of least prime signature frequently are adjacent to primes (see A344385). It appears to be far more rare for a number of least prime signature to be at the center of a maximal prime gap. With 4 being a term in A344385, 120 seems to have a unique status. - Hal M. Switkay, Mar 13 2025

Links

• Hugo Pfoertner, Table of n, a(n) for n = 2..83
• Hugo Pfoertner, Gap sizes vs location, using Plot 2.

Crossrefs

Subsequence of A024675.

Cf. A000040, A000101, A002386, A344385.