A071184 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*(n+1)/2 the n-th triangular number.

1, 2, 8, 10, 60, 75, 131, 195, 988, 1120, 1130, 1232, 1345, 1347, 1953, 2933, 3549, 9956, 13797, 13970, 14586, 14652, 14903, 17166, 19176, 19634, 22584, 24354, 24842, 26488, 29388, 30840, 31409, 34934, 36059, 45149, 49793, 52690, 59413, 61063

Offset

1,2

Links

Table of n, a(n) for n=1..40.

Example

1/a(1)+1/a(2)+1/a(3)+1/a(4) = (1+1/2+1/8+1/10) which continued fraction is {1, 1, 2, 1, 1, 1, 3} and 1+1+2+1+1+1+3 = 10 = 4*5/2 the fourth triangular number.

Prog

(PARI) s=1; t=1; for(n=2, 22, s=s+1/t; while(abs(n*(n+1)/2+1-sum(i=1, length(contfrac(s+1/t)), component(contfrac(s+1/t), i)))>0, t++); print1(t, ", "))

Crossrefs

Sequence in context: A107227 A188539 A230826 * A174153 A171976 A362278

Adjacent sequences: A071181 A071182 A071183 * A071185 A071186 A071187

Keyword

easy,nonn

Author

Benoit Cloitre, Jun 10 2002

Extensions

More terms from Lambert Klasen (lambert.klasen(AT)gmx.de), Dec 18 2004

Status

approved