A114990 a(n) = a(n-2) + A000265(a(n-1)), a(0)=0, a(1)=1.

0, 1, 1, 2, 2, 3, 5, 8, 6, 11, 17, 28, 24, 31, 55, 86, 98, 135, 233, 368, 256, 369, 625, 994, 1122, 1555, 2677, 4232, 3206, 5835, 9041, 14876, 12760, 16471, 29231, 45702, 52082, 71743, 123825, 195568, 136048, 204071, 340119, 544190, 612214, 850297, 1462511

Offset

0,4

Comments

The sequence is clearly not monotonic, but the subsequences with even resp. odd indices are both strictly increasing. The sequence is obviously bounded above by the Fibonacci sequence A000045. The subsequence of n-th terms, where n is congruent to 2 or 3 mod 4, is bounded below by the Fibonacci sequence; therefore a(2n)>f(n) for n>1. - Joseph Pedersen (jmp456(AT)psu.edu), Feb 27 2006, rephrased by M. F. Hasler, Feb 18 2013

Links

Table of n, a(n) for n=0..46.

Example

The highest odd integer dividing a(11)=28 is 7. So a(12) = a(10) + 7 = 17 + 7 = 24.
The greatest odd divisor of a(11)=28 is 7, so a(12)= a(10)+7 = 17+7 = 24.

Prog

(PARI) A114990(n, print_all=0, a=1, o=0)={n||a=o; for(n=2, n, print_all&print1(a", "); a=o+a>>valuation(o=a, 2)); a} \\ Old versions (<= 2.4) of PARI might require to write o+0+a>>... - M. F. Hasler, Feb 18 2013

Crossrefs

Cf. A000265.

Sequence in context: A253853 A127678 A199962 * A241421 A157176 A276429

Adjacent sequences: A114987 A114988 A114989 * A114991 A114992 A114993

Keyword

easy,nonn

Author

Leroy Quet, Feb 22 2006

Extensions

More terms from Joseph Pedersen (jmp456(AT)psu.edu) and Amy Postell (arp179(AT)psu.edu), Feb 27 2006

Edited & initial term a(0)=0 added by M. F. Hasler, Feb 18 2013

Status

approved