A360097 a(n) = smallest k such that 2*n*k-1 and 2*n*k+1 are nonprimes.

13, 14, 20, 7, 5, 10, 4, 4, 8, 6, 7, 5, 1, 2, 4, 2, 1, 4, 2, 3, 17, 4, 2, 3, 1, 4, 4, 1, 2, 2, 2, 1, 8, 3, 8, 2, 4, 1, 8, 2, 3, 11, 1, 2, 10, 1, 1, 3, 4, 3, 2, 2, 4, 2, 2, 5, 3, 1, 1, 1, 1, 1, 9, 4, 2, 4, 1, 4, 3, 4, 1, 1, 1, 2, 2, 2, 1, 4, 3, 1, 2, 2, 4, 7, 1

Offset

1,1

Links

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

Example

We try 1..k until the condition is met:
a(7) != 1 because 2*7*1 = 14 and 14 - 1 = 13, a prime.
a(7) != 2 because 2*7*2 = 28 and 28 + 1 = 29, a prime.
a(7) != 3 because 2*7*3 = 42 and 42 - 1 = 41 and 42 + 1 = 43, both primes.
a(7) = 4 because 2*7*4 = 56 and 56 - 1 = 55 and 56 + 1 = 57 are both nonprimes.

Maple

f:= proc(n) local k;
    for k from 1 do
      if not isprime(2*n*k-1) and not isprime(2*n*k+1) then return k fi
    od
end proc:
map(f, [$1..100]); # Robert Israel, Feb 07 2023

Mathematica

a[n_] := Module[{k = 1}, While[PrimeQ[2*n*k - 1] || PrimeQ[2*n*k + 1], k++]; k]; Array[a, 100] (* Amiram Eldar, Jan 25 2023 *)

Prog

(Python)
from sympy import isprime
from itertools import count
def a(n): return next(k for k in count(1) if not isprime(2*n*k-1) and not isprime(2*n*k+1))
print([a(n) for n in range(1, 86)]) # Michael S. Branicky, Jan 25 2023
(PARI) a(n) = my(k=1); while(isprime(2*n*k-1) || isprime(2*n*k+1), k++); k; \\ Michel Marcus, Jan 25 2023

Crossrefs

Cf. A018252, A124522.

Sequence in context: A241749 A098045 A293817 * A360258 A360528 A336004

Adjacent sequences: A360094 A360095 A360096 * A360098 A360099 A360100

Keyword

nonn

Author

Tamas Sandor Nagy, Jan 25 2023

Extensions

More terms from Michael S. Branicky, Jan 25 2023

Status

approved