A163981 a(n) is the smallest prime of the form prime(n+1)*k - prime(n), k >= 1, where prime(n) is the n-th prime.

7, 2, 2, 37, 2, 89, 2, 73, 151, 2, 43, 127, 2, 239, 59, 419, 2, 73, 359, 2, 401, 419, 1163, 881, 307, 2, 967, 2, 569, 3697, 397, 691, 2, 457, 2, 163, 821, 839, 179, 1259, 2, 2111, 2, 1777, 2, 223, 3803, 3863, 2, 3499, 1201, 2, 2269, 263, 269, 1889, 2, 283, 1409, 2, 2647

Offset: 1

Author

Leroy Quet, Aug 07 2009

Keywords

• nonn

Comments

a(n) = 2 if and only if n is in A029707. - Robert Israel, Jan 16 2019

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A029707, A129919.

Contains A085704.

Programs

Maple

a := proc (n) local k: for k while isprime(ithprime(n+1)*k-ithprime(n)) = false do end do: ithprime(n+1)*k-ithprime(n) end proc: seq(a(n), n = 1 .. 65); # Emeric Deutsch, Aug 10 2009

Mathematica

a[n_] := Module[{p, q, r}, For[p = Prime[n]; q = Prime[n + 1]; k = 1, True, k++, If[PrimeQ[r = q k - p], Return[r]]]];
Array[a, 100] (* Jean-François Alcover, Aug 28 2020 *)

PARI

a(n) = my(k=1); while (!isprime(p=prime(n+1)*k - prime(n)), k++); p; \\ Michel Marcus, Jul 02 2021

Python

from sympy import isprime, nextprime, prime
def a(n):
    pn = prime(n); pn1 = nextprime(pn); k = 1
    while not isprime(pn1*k - pn): k += 1
    return pn1*k - pn
print([a(n) for n in range(1, 62)]) # Michael S. Branicky, Jul 02 2021

Extensions

Extended by Emeric Deutsch, Aug 10 2009