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A215095
a(0)=0, a(1)=1, a(n) = least k>a(n-1) such that k+a(n-2) is a Jacobsthal number.
1
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.
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, end=', ')
b = c = 0
while c<=prev:
c = jac[b] - prpr
b+=1
prpr = prev
prev = c
CROSSREFS
KEYWORD
nonn
AUTHOR
Alex Ratushnyak, Aug 03 2012
STATUS
approved