A254498 Define a(1)=2 and a(2)=3. Then, if a(n-2) and a(n-1) have the same parity, a(n)=(a(n-2)+a(n-1))/2; if not, a(n)=a(n-2)/2+a(n-1) for a(n-2) even or a(n)=a(n-2)+a(n-1)/2 for a(n-1) even.

2, 3, 4, 5, 7, 6, 10, 8, 9, 13, 11, 12, 17, 23, 20, 33, 43, 38, 62, 50, 56, 53, 81, 67, 74, 104, 89, 141, 115, 128, 179, 243, 211, 227, 219, 223, 221, 222, 332, 277, 443, 360, 623, 803, 713, 758, 1092, 925, 1471, 1198, 2070, 1634, 1852, 1743, 2669, 2206, 3772

Offset

1,1

Comments

If we start with a(1)=a(2)=2, then a(n)=2 for every n.

As N increases, sum_{n=1..N} 1/a(n) converges quickly to

2.6332482094949767034995557279162460374965915768...

More generally, if one starts with a(1) = a(2), then a(n) = a(1) for every n.

Links

Pierre CAMI, Table of n, a(n) for n = 1..1000

Example

As 2 is even and 3 is odd, a(4) = 2/2 + 3 = 4.
As 3 is odd and 4 is even, a(5) = 3 + 4/2 = 5.

Mathematica

a[n_] := a[n] = If[ Mod[ a[n - 1], 2] == Mod[ a[n - 2], 2], (a[n - 1] + a[n - 2])/2, If[ OddQ@ a[n - 1], a[n - 1] + a[n - 2]/2, a[n - 1]/2 + a[n - 2]]]; a[1] = 2; a[2] = 3; a = Array[a, 69] (* Robert G. Wilson v, Mar 11 2015 *)

Prog

(PFGW & SCRIPT)
SCRIPT
DIM i, 0
DIM j, 4
DIM k
DIM n, 1
OPENFILEOUT myf, seq.txt
WRITE myf, i
WRITE myf, j
LABEL loop1
SET n, n+1
IF n>1000 THEN END
IF i%2==0 && j%2==0 THEN SET k, (i+j)/2
IF i%2==1 && j%2==1 THEN SET k, (i+j)/2
IF i%2==0 && j%2==1 THEN SET k, i/2+j
IF i%2==1 && j%2==0 THEN SET k, i+j/2
WRITE myf, k
SET i, j
SET j, k
GOTO loop1
(PARI) a(n, a=0, b=4)={n||return(a); for(i=2, n, b=if((b-a)%2, if(a%2, a+(a=b)\2, a\2+a=b), (a+a=b)\2)); b} \\ M. F. Hasler, Feb 10 2015

Crossrefs

Cf. A254330.

Sequence in context: A256231 A288870 A283194 * A185969 A369281 A266637

Adjacent sequences: A254495 A254496 A254497 * A254499 A254500 A254501

Keyword

nonn

Author

Pierre CAMI, Jan 31 2015

Status

approved