A145103 a(0) = a(1) = 1. a(n+1) = ceiling(n*a(n)/a(n-1)), for n >= 1.

1, 1, 1, 2, 6, 12, 10, 5, 4, 7, 16, 23, 16, 9, 8, 13, 25, 31, 22, 13, 12, 19, 34, 40, 28, 17, 16, 25, 43, 49, 34, 21, 20, 31, 52, 58, 40, 25, 24, 37, 61, 66, 45, 29, 28, 43, 70, 75, 51, 33, 32, 49, 79, 84, 57, 37, 36, 55, 88, 93, 63, 41, 40, 61, 97, 102, 69, 45, 44, 67, 106, 111

Offset: 0

Author

Leroy Quet, Oct 01 2008

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,-1,1,-1,1,1,-1,1,-1,1,-1).

Crossrefs

Cf. A145102.

Programs

Maple

A[0]:= 1: A[1]:= 1:
for n from 1 to 99 do A[n+1]:= ceil(n*A[n]/A[n-1]) od:
seq(A[i],i=0..100); # Robert Israel, Dec 06 2022

Mathematica

nxt[{n_,a_,b_}]:={n+1,b,Ceiling[((n+1)b)/a]}; Join[{1},Transpose[ NestList[ nxt,{0,1,1},80]][[3]]] (* Harvey P. Dale, Mar 04 2013 *)

PARI

print1(a=1, ",", b=1, ","); for(n=2, 71, print1(c=ceil((n-1)*b/a), ","); a=b; b=c) \\ Klaus Brockhaus, Oct 02 2008

PARI

a(n)=if(n<37, return([1, 1, 1, 2, 6, 12, 10, 5, 4, 7, 16, 23, 16, 9, 8, 13, 25, 31, 22, 13, 12, 19, 34, 40, 28, 17, 16, 25, 43, 49, 34, 21, 20, 31, 52, 58, 40][n+1])); my(r=n%6,k=n\6); if(r==0, 6*k+3, r==1, 4*k+1, r==2, 4*k, r==3, 6*k+1, r==4, 9*k+7, 9*k+12) \\ Charles R Greathouse IV, Dec 07 2022

Formula

From Robert Israel, Dec 06 2022: (Start)

a(6*k) = 6*k+3 for k >= 7.

a(6*k+1) = 4*k+1.

a(6*k+2) = 4*k for k >= 1.

a(6*k+3) = 6*k+1 for k >= 1.

a(6*k+4) = 9*k+7 for k >= 1.

a(6*k+5) = 9*k+12 for k >= 6.

(End)

Extensions

More terms from Klaus Brockhaus and R. J. Mathar, Oct 02 2008