A392470 Record values of minimum k in the Erdős-Straus y = k*p construction for 4/p = 1/x + 1/y + 1/z.

2, 4, 8, 12, 25, 39, 42, 48, 65, 70, 72, 76, 84, 96, 624, 816, 950, 957, 966, 990, 1484, 1833

Offset

1,1

Comments

a(n) is the minimum k required for the n-th record-breaking prime A392469(n).

Note dramatic jumps: a(14)=96 to a(15)=624 (6.5x), and a(20)=990 to a(21)=1484 (1.5x).

The ratio a(n)/log(A392469(n)) appears bounded by 71, with maximum 70.59 at n=22.

Verified by GPU search to 10^13 as of Jan 2026.

Links

Table of n, a(n) for n=1..22.

Wikipedia, Erdős-Straus conjecture.

Example

a(1) = 2 for prime A392469(1) = 73.
a(15) = 624 for prime A392469(15) = 2031121.
a(22) = 1833 for prime A392469(22) = 189241671529.

Crossrefs

Cf. A392469 (corresponding primes), A073101, A075245, A075246.

Sequence in context: A115386 A306491 A058771 * A385147 A358512 A036493

Adjacent sequences: A392467 A392468 A392469 * A392471 A392472 A392473

Keyword

nonn,hard,more

Author

Jeffrey H. Gold, Jan 13 2026

Status

approved