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a(0)=0, a(1)=1, a(n) = least k>a(n-1) such that k+a(n-2) is prime.
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%I #17 Nov 10 2024 16:00:50

%S 0,1,2,4,5,7,8,10,11,13,18,24,25,29,34,38,39,41,44,48,53,55,56,58,71,

%T 73,78,84,85,89,94,102,103,109,120,124,131,133,138,144,145,149,162,

%U 164,169,173,178,180,181,187,192,196,197,201

%N a(0)=0, a(1)=1, a(n) = least k>a(n-1) such that k+a(n-2) is prime.

%C For n>0 and (n mod 4)<2, a(n) is odd.

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

%C Fibonacci number: A006498 except first two terms,

%C Lucas number: A000045 except first two terms,

%C Pell number: A089928(n-1),

%C Jacobsthal number: A215095,

%C factorial: A215096,

%C square: A194274,

%C cube: A215097,

%C triangular number: A011848(n+2),

%C oblong number: A215098.

%C 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.

%H Iain Fox, <a href="/A215099/b215099.txt">Table of n, a(n) for n = 0..10000</a>

%o (Python)

%o from sympy import prime

%o prpr = 0

%o prev = 1

%o for n in range(77):

%o print(prpr, end=', ')

%o b = c = 0

%o while c<=prev:

%o c = prime(b+1) - prpr

%o b+=1

%o prpr = prev

%o prev = c

%o (PARI) first(n) = my(res = vector(n, i, i-1), k); for(x=3, n, k=res[x-1]+1; while(!isprime(k+res[x-2]), k++); res[x]=k); res \\ _Iain Fox_, Apr 22 2019 (corrected by _Iain Fox_, Apr 25 2019)

%Y Cf. A062042: a(1) = 2, a(n) = least k>a(n-1) such that k+a(n-1) is a prime.

%Y Cf. A073627, A073628.

%K nonn

%O 0,3

%A _Alex Ratushnyak_, Aug 03 2012