A330248 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.

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, 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, 1, 0, 0, 1, 5, 0, 4, 3, 3, 2, 2, 1, 1, 0, 0, 5, 7, 4, 6

Offset: 1

Author

Ali Sada, Dec 06 2019

Keywords

• nonn

Comments

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, ...

Examples

			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.
		

Crossrefs

Cf. A062042.

Programs

Mathematica

Nest[Append[#1, Block[{k = 0}, While[! PrimeQ[#1[[-1]] + k + #2], k++]; k]] & @@ {#, Length@ # + 1} &, {1}, 105] (* Michael De Vlieger, Dec 14 2019 *)

PARI

for (n=1, 87, print1 (v=if (n==1, 1, nextprime(n+v)-n-v)", ")) \\ Rémy Sigrist, Dec 06 2019