A070904 - OEIS

%I #16 Apr 05 2020 05:01:29

%S 1,16,20976,50649,51933,86768,99857,442973,547720,1374279,6529369,

%T 15997726,16615151,18691278,30371349,43665242,75220431

%N a(1) = 1, a(n) is the smallest integer > a(n-1) such that the largest element in the simple continued fraction for S(n) = 1/a(1) + 1/a(2) + ... + 1/a(n) equals n^4.

%e The continued fraction for S(5) = 1 + 1/16 + 1/20976 + 1/50649 + 1/51933 is [1, 15, 1, 44, 7, 1, 1, 1, 1, 3, 2, 2, 3, 1, 6, 3, 1, 625, 2, 4] where the largest element is 625 = 5^4 and 51933 is the smallest integer > 50649 with this property.

%o (PARI) s=1; t=1; for(n=2, 17, s=s+1/t; while(abs(n^4-vecmax(contfrac(s+1/t)))>0, t++); print1(t, ", "))

%Y Cf. A070902, A070903.

%K nonn,more

%O 1,2

%A _Benoit Cloitre_, May 19 2002

%E a(11)-a(16) from _Ryan Propper_, Aug 06 2005

%E a(17) from _Jinyuan Wang_, Apr 05 2020