A059534 Beatty sequence for 1 + 1/Catalan's constant.

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133

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.

Index entries for sequences related to Beatty sequences

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

Beatty complement is A059533.

Cf. A006752.

Sequence in context: A147819 A230201 A373787 * A137804 A246414 A054965

Adjacent sequences: A059531 A059532 A059533 * A059535 A059536 A059537

Keyword

nonn,easy

Author

Mitch Harris, Jan 22 2001

Status

approved