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%I #18 Jan 06 2020 21:31:08
%S 1,0,0,1,1,0,0,3,1,0,0,1,3,0,2,1,1,0,0,3,5,2,4,1,3,0,2,1,1,0,0,5,3,0,
%T 2,3,1,2,0,1,1,0,0,3,5,2,4,1,3,0,2,5,1,4,0,3,1,0,0,1,5,0,4,3,3,2,2,1,
%U 1,0,0,1,5,0,4,3,3,2,2,1,1,0,0,5,7,4,6
%N a(1) = 1; for n > 1, a(n) is the least nonnegative number such that a(n) + a(n-1) + n is a prime number.
%C The primes that result from this sequence are 3, 3, 5, 7, 7, 7, 11, 13, 11, 11, 13, 17, 17, 17, 19, 19, 19, 19, 23, 29, 29, 29, 29, 29, 29, 29, 31, 31, 31, 31, 37, 41, 37, 37, 41, ...
%e When n=5, a(4)=1; we want a(5)+a(4)+5 to be a prime. 1 is the least nonnegative number that satisfies this condition (1+5+1=7). So, a(5)=1.
%t Nest[Append[#1, Block[{k = 0}, While[! PrimeQ[#1[[-1]] + k + #2], k++]; k]] & @@ {#, Length@ # + 1} &, {1}, 105] (* _Michael De Vlieger_, Dec 14 2019 *)
%o (PARI) for (n=1, 87, print1 (v=if (n==1, 1, nextprime(n+v)-n-v)", ")) \\ _Rémy Sigrist_, Dec 06 2019
%Y Cf. A062042.
%K nonn
%O 1,8
%A _Ali Sada_, Dec 06 2019