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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.

%I A215095 #18 Oct 01 2024 15:44:55
%S A215095 0,1,3,4,8,17,35,68,136,273,547,1092,2184,4369,8739,17476,34952,69905,
%T A215095 139811,279620,559240,1118481,2236963,4473924,8947848,17895697,
%U A215095 35791395,71582788,143165576,286331153,572662307,1145324612,2290649224,4581298449,9162596899
%N A215095 a(0)=0, a(1)=1, a(n) = least k>a(n-1) such that k+a(n-2) is a Jacobsthal number.
%C A215095 Same definition, but k+a(n-2) is a
%C A215095 Fibonacci number: A006498 except first two terms,
%C A215095 Lucas number: A000045 except first two terms,
%C A215095 Pell number: A089928(n-1),
%C A215095 factorial: A215096,
%C A215095 square: A194274,
%C A215095 cube: A215097,
%C A215095 triangular number: A011848(n+2),
%C A215095 oblong number: A215098,
%C A215095 prime number: A215099.
%C A215095 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.
%F A215095 Conjecture: G.f. (x+2*x^2)/(1-x-x^2-x^3-2*x^4). - _David Scambler_, Aug 06 2012
%o A215095 (Python)
%o A215095 prpr = 0
%o A215095 prev = 1
%o A215095 jac = [0]*10000
%o A215095 for n in range(10000):
%o A215095     jac[n] = prpr
%o A215095     curr = prpr*2 + prev
%o A215095     prpr = prev
%o A215095     prev = curr
%o A215095 prpr, prev = 0, 1
%o A215095 for n in range(1, 44):
%o A215095     print(prpr, end=', ')
%o A215095     b = c = 0
%o A215095     while c<=prev:
%o A215095         c = jac[b] - prpr
%o A215095         b+=1
%o A215095     prpr = prev
%o A215095     prev = c
%Y A215095 Cf. A001045, A006498, A089928, A000045.
%K A215095 nonn
%O A215095 0,3
%A A215095 _Alex Ratushnyak_, Aug 03 2012