A071972 a(1)=1, a(n) is the smallest integer > a(n-1) such that the sum of elements of the simple continued fraction for S(n)=1/a(1)+1/a(2)+...+1/a(n) equals n^4.

1, 15, 1339, 6069, 28879, 40941, 66183, 77707, 1359489, 1651008, 7923801, 16146690, 22400968

Offset

1,2

Links

Table of n, a(n) for n=1..13.

Example

1/a(1)+1/a(2)+1/a(3)+1/a(4) = (1+1/15+1/1339+1/6069) which continued fraction is {1, 14, 1, 3, 1, 16, 3, 1, 1, 1, 4, 210} and 1+14+1+3+1+16+3+1+1+1+4+210 = 256 = 4^4.

Mathematica

a[1] = 1; a[n_] := a[n] = (s = Sum[1/a[i], {i, 1, n - 1}]; While[Plus @@ ContinuedFraction[s + 1/k] != n^4, k++ ]; k); k = 1; Do[ Print[ a[n]], {n, 1, 14}]

Prog

(PARI) s=1; t=1; for(n=2, 14, s=s+1/t; while(abs(n^4+1-sum(i=1, length(contfrac(s+1/t)), component(contfrac(s+1/t), i)))>0, t++); print1(t, ", "))

Crossrefs

Cf. A071183.

Sequence in context: A232147 A232288 A183550 * A350994 A206376 A331465

Adjacent sequences: A071969 A071970 A071971 * A071973 A071974 A071975

Keyword

nonn

Author

Robert G. Wilson v, Jun 17 2002

Status

approved