A108906 First differences of A006899.

1, 1, 1, 4, 1, 7, 11, 5, 32, 17, 47, 115, 13, 256, 217, 295, 1024, 139, 1909, 2465, 1631, 8192, 3299, 13085, 26281, 6487, 65536, 46075, 84997, 262144, 7153, 517135, 545747, 502829, 2097152, 588665, 3605639, 5960299, 2428309, 16777216, 9492289

Offset

1,4

Comments

In the 14th century Levi Ben Gerson proved that this sequence contains only four 1s; see A235365, A235366, A236210. - Jonathan Sondow, Jan 20 2014

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Maple

A:={seq(2^n, n=0..63)}: B:={seq(3^n, n=0..40)}: C:=sort(convert(A union B, list)): seq(C[j]-C[j-1], j=2..44); # Emeric Deutsch, Aug 03 2005

Mathematica

nn = 10^20; t = Union[ 2^Range[0, Floor[Log[2, nn]]], 3^Range[0, Floor[Log[3, nn]]]]; Differences@ t (* Robert G. Wilson v, May 26 2014 *)

Prog

(Haskell)
a108906 n = a108906_list !! (n-1)
a108906_list = zipWith (-) (tail a006899_list) a006899_list
-- Reinhard Zumkeller, Oct 09 2013
(Python)
from sympy import integer_log
def A108906(n):
    m, m2 = 3**(n-1), 1<<n
    k, k2, k3 = integer_log(m, 6)[0], integer_log(3*m, 6)[0], integer_log(9*m, 6)[0]
    return (1<<k2 if k2<k3 else 3**integer_log(m2<<1, 6)[0]-(1<<k2)) if k<k2 else ((1<<k3)-3**integer_log(m2, 6)[0] if k2<k3 else 3**integer_log(m2<<1, 6)[0]-3**integer_log(m2, 6)[0]) # Chai Wah Wu, Oct 01 2024

Crossrefs

Cf. A006899.

Cf. also A235365, A235366, A236210.

Sequence in context: A050411 A010643 A377344 * A193842 A134250 A139045

Adjacent sequences: A108903 A108904 A108905 * A108907 A108908 A108909

Keyword

easy,nonn

Author

Ali A. Tanara (tanara(AT)khayam.ut.ac.ir), Jul 17 2005

Extensions

More terms from Emeric Deutsch, Aug 03 2005

Status

approved