A215095 a(0)=0, a(1)=1, a(n) = least k>a(n-1) such that k+a(n-2) is a Jacobsthal number.

0, 1, 3, 4, 8, 17, 35, 68, 136, 273, 547, 1092, 2184, 4369, 8739, 17476, 34952, 69905, 139811, 279620, 559240, 1118481, 2236963, 4473924, 8947848, 17895697, 35791395, 71582788, 143165576, 286331153, 572662307, 1145324612, 2290649224, 4581298449, 9162596899

Offset

0,3

Comments

Same definition, but k+a(n-2) is a

Fibonacci number: A006498 except first two terms,

Lucas number: A000045 except first two terms,

Pell number: A089928(n-1),

factorial: A215096,

square: A194274,

cube: A215097,

triangular number: A011848(n+2),

oblong number: A215098,

prime number: A215099.

Example of a related sequence definition: a(0)=0, a(1)=1, a(n) = least k>a(n-1) such that k+a(n-2) is a cube.

Links

Table of n, a(n) for n=0..34.

Formula

Conjecture: G.f. (x+2*x^2)/(1-x-x^2-x^3-2*x^4). - David Scambler, Aug 06 2012

Prog

(Python)
prpr = 0
prev = 1
jac = [0]*10000
for n in range(10000):
    jac[n] = prpr
    curr = prpr*2 + prev
    prpr = prev
    prev = curr
prpr, prev = 0, 1
for n in range(1, 44):
    print prpr,
    b = c = 0
    while c<=prev:
        c = jac[b] - prpr
        b+=1
    prpr = prev
    prev = c

Crossrefs

Cf. A001045, A006498, A089928, A000045.

Sequence in context: A049894 A198633 A153057 * A192474 A183494 A107429

Adjacent sequences: A215092 A215093 A215094 * A215096 A215097 A215098

Keyword

nonn

Author

Alex Ratushnyak, Aug 03 2012

Status

approved