A136048 -id:A136048 - cp's OEIS frontend

A135439 Positions of A136048(n) in A136047.

9, 13, 14, 17, 18, 22, 26, 29, 30, 33, 37, 41, 45, 58, 65, 66, 73, 77, 78, 81, 102, 105, 113, 121, 122, 134, 141, 142, 145, 174, 178, 185, 186, 193, 206, 214, 221, 225, 246, 257, 261, 274, 281, 302, 314, 318, 357, 358, 366, 393, 397, 402, 425, 437

Offset: 1

Zak Seidov, Dec 15 2007

nonn

A136047 a(1)=1, a(n)=a(n-1)+n if n even, a(n)=a(n-1)+n^2 if n is odd.

Original entry on oeis.org

1, 3, 12, 16, 41, 47, 96, 104, 185, 195, 316, 328, 497, 511, 736, 752, 1041, 1059, 1420, 1440, 1881, 1903, 2432, 2456, 3081, 3107, 3836, 3864, 4705, 4735, 5696, 5728, 6817, 6851, 8076, 8112, 9481, 9519, 11040, 11080, 12761, 12803, 14652, 14696, 16721

Offset: 1

Zak Seidov, Dec 12 2007

The only prime terms are 3, 41, 47.
The semiprime terms are A136048.
Cf. A001082/A135370: f(1) = 1, then if n even/odd f(n) = n+f(n-1), if n odd/even f(n) = 2*n+f(n-1).

Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).

Cf. A001082, A135370, A136048.

a[1]=1;a[n_]:=a[n]=a[n-1]+n^(1+Mod[n,2]); Table[a[n],{n,100}]
nxt[{n_,a_}]:={n+1,If[OddQ[n],a+n+1,a+(n+1)^2]}; Transpose[NestList[nxt,{1,1},50]][[2]] (* Harvey P. Dale, Oct 11 2015 *)

a(n) = (1/12)(1 + n)(2n^2+7n-3) if n is odd, a(n)=(1/12)n(2n^2+3n+4) if n is even.
a(n) = (-3 + 3*(-1)^n + 8*n + 12*n^2 - 6*(-1)^n*n^2 + 4*n^3)/24.
a(1)=1 then a(n) = a(n-1)+n^(if n is even then 1 else 2),
         or a(n) = a(n-1)+n^(1+mod(n,2)),
         or a(n) = a(n-1)+n^((3-(-1)^n)/2).
From R. J. Mathar, Feb 22 2009: (Start)
a(n) = a(n-1)+3*a(n-2)-3*a(n-3)-3*a(n-4)+3*a(n-5)+a(n-6)-a(n-7).
G.f.: x*(1+2*x+6*x^2-2*x^3+x^4)/((1+x)^3*(x-1)^4). (End)

Edited by Michel Marcus, Mar 02 2022

cp's OEIS Frontend

A135439 Positions of A136048(n) in A136047.

Views

Author

Keywords

A136047 a(1)=1, a(n)=a(n-1)+n if n even, a(n)=a(n-1)+n^2 if n is odd.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

Extensions