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

Author

Alex Ratushnyak, Aug 03 2012

Keywords

• nonn

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.

Crossrefs

Cf. A001045, A006498, A089928, A000045.

Programs

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, end=', ')
    b = c = 0
    while c<=prev:
        c = jac[b] - prpr
        b+=1
    prpr = prev
    prev = c

Formula

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