A059533 Beatty sequence for 1 + Catalan's constant.

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 114, 116, 118, 120, 122, 124

Offset

1,2

Links

Harry J. Smith, Table of n, a(n) for n = 1..2000

Aviezri S. Fraenkel, Jonathan Levitt, 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

Index entries for sequences related to Beatty sequences

Formula

a(n) = floor(n*(1+A006752)). - R. J. Mathar, May 22 2019

Prog

(PARI) { digits=100; default(realprecision, digits+80); s=1.0; n=5*digits; 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 + s; for (n = 1, 2000, write("b059533.txt", n, " ", floor(n*b)); ) } \\ Harry J. Smith, Jun 27 2009

Crossrefs

Beatty complement is A059534.

Sequence in context: A064719 A214657 A137803 * A189397 A172100 A064679

Adjacent sequences: A059530 A059531 A059532 * A059534 A059535 A059536

Keyword

nonn,easy

Author

Mitch Harris, Jan 22 2001

Status

approved