A343070 a(1) = 1, for n > 1, a(n) is the smallest positive integer for which a(n-1) + n + a(n) is a prime.

1, 2, 2, 1, 1, 4, 2, 1, 1, 2, 4, 1, 3, 2, 2, 1, 1, 4, 6, 3, 5, 2, 4, 1, 3, 2, 2, 1, 1, 6, 4, 1, 3, 4, 2, 3, 1, 2, 2, 1, 1, 4, 6, 3, 5, 2, 4, 1, 3, 6, 2, 5, 1, 4, 2, 1, 1, 2, 6, 1, 5, 4, 4, 3, 3, 2, 2, 1, 1, 2, 6, 1, 5, 4, 4, 3, 3, 2, 2, 1, 1, 6, 8

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Todor Szimeonov, A completive sequence

Mathematica

a[1] = 1; a[n_] := a[n] = NextPrime[a[n - 1] + n] - a[n - 1] - n; Array[a, 100] (* Amiram Eldar, Apr 04 2021 *)
nxt[{n_, a_}]:={n+1, NextPrime[a+n+1]-a-n-1}; NestList[nxt, {1, 1}, 100][[;; , 2]] (* Harvey P. Dale, Oct 19 2025 *)

Prog

(Python)
from sympy import nextprime
def aupton(terms):
  alst = [1]
  for n in range(2, terms+1):
    alst.append(nextprime(alst[-1] + n) - alst[-1] - n)
  return alst
print(aupton(87)) # Michael S. Branicky, Apr 04 2021

Crossrefs

Cf. A343039.

Sequence in context: A100996 A232504 A292201 * A090048 A064285 A006694

Adjacent sequences: A343067 A343068 A343069 * A343071 A343072 A343073

Keyword

nonn

Author

Todor Szimeonov, Apr 04 2021

Status

approved