A133470 Numbers k > 1 for which floor(b(k)) = floor(b(k-1)), where b(m) = Sum_{j=1..m} (j/(j+2)).

2, 5, 9, 17, 29, 49, 81, 135, 225, 371, 614, 1013, 1672, 2757, 4548, 7499, 12365, 20388, 33615, 55423, 91378, 150659, 248395, 409536, 675212, 1113237, 1835419, 3026095, 4989189, 8225783, 13562025, 22360001, 36865410, 60780788, 100210579, 165219314, 272400598, 449112661

Offset

1,1

Comments

I conjecture that lim_{n->infinity} a(n)/a(n-1) = sqrt(e). For integers not in the sequence, b(m) = 1 + b(m-1).

Links

Table of n, a(n) for n=1..38.

Example

floor(b(1)) = floor(1/3) = 0;
floor(b(2)) = floor(1/3 + 2/4) = 0;
hence 2 is a term.

Prog

(PARI) A=0; for(n=1, 1000000, B=A; A=B+(n/(n+2)); if(floor(A)-floor(B)-1, print1(n, ", ")))

Crossrefs

Sequence in context: A034329 A230441 A340668 * A129696 A082281 A285458

Adjacent sequences: A133467 A133468 A133469 * A133471 A133472 A133473

Keyword

easy,nonn

Author

Philippe LALLOUET (philip.lallouet(AT)orange.fr), Nov 28 2007

Extensions

More terms from Hugo Pfoertner, Jul 04 2021

Status

approved