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
Keywords
Examples
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.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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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 *) -
PARI
a(n) = my(k=1); while(isprime(2*n*k-1) || isprime(2*n*k+1), k++); k; \\ Michel Marcus, Jan 25 2023
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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
Extensions
More terms from Michael S. Branicky, Jan 25 2023