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

1,8

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, ...

Links

Table of n, a(n) for n=1..87.

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A062042.

Sequence in context: A269246 A334566 A342270 * A247505 A117389 A122083

Adjacent sequences: A330245 A330246 A330247 * A330249 A330250 A330251

Keyword

nonn

Author

Ali Sada, Dec 06 2019

Status

approved