OFFSET
1,1
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..2000
Aviezri S. Fraenkel, Jonathan Levitt, and Michael Shimshoni, Characterization of the set of values f(n)=[n alpha], n=1,2,..., Discrete Math. 2 (1972), no.4, 335-345.
Eric Weisstein's World of Mathematics, Beatty Sequence.
FORMULA
a(n) = floor(n*(1 + 1/A006752)). - Paolo Xausa, Jul 05 2024
MATHEMATICA
Floor[Range[100]*(1 + 1/Catalan)] (* Paolo Xausa, Jul 05 2024 *)
PROG
(PARI) { numdigits=100; default(realprecision, numdigits+80); s=1.0; n=5*numdigits; j=4*n+1; si=-1.0; for (i=3, j-2, s+=si/i^2; si=-si; i++; ); s+=0.5/j^2; ttk=4.0; d=4.0*j^3; xk=2.0; xkp=xk; for (k=2, 100000000, term=(ttk-1)*ttk*xkp; xk++; xkp*=xk; if (k>2, term*=xk; xk++; xkp*=xk; ); term*=bernreal(k)/d; sn=s+term; if (sn==s, break); s=sn; ttk*=4.0; d*=(k+1)*(k+2)*j^2; k++; ); b=1 + 1/s; for (n = 1, 2000, write("b059534.txt", n, " ", floor(n*b)); ) } \\ Harry J. Smith, Jun 27 2009
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mitch Harris, Jan 22 2001
STATUS
approved