A392470 - OEIS

%I #8 Jan 18 2026 21:00:38

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

%T 1833

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

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

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

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

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Straus_conjecture">Erdős-Straus conjecture</a>.

%e a(1) = 2 for prime A392469(1) = 73.

%e a(15) = 624 for prime A392469(15) = 2031121.

%e a(22) = 1833 for prime A392469(22) = 189241671529.

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

%K nonn,hard,more

%O 1,1

%A _Jeffrey H. Gold_, Jan 13 2026