[go: up one dir, main page]

login
A175452
a(n) = smallest prime such that a(n)+2 is multiple of 2n+1.
1
7, 3, 5, 7, 31, 11, 13, 83, 17, 19, 67, 23, 79, 317, 29, 31, 103, 109, 37, 367, 41, 43, 139, 47, 151, 157, 53, 283, 293, 59, 61, 193, 199, 67, 211, 71, 73, 229, 709, 79, 911, 83, 433, 443, 89, 277, 283, 677, 97, 503, 101, 103, 2459, 107, 109, 337, 113, 349, 593, 1087
OFFSET
1,1
COMMENTS
Terms appearing twice: a(1)=a(4)=7, a(5)=a(16)=31,...,
terms appearing thrice: a(28)=a(47)=a(142)=283, a(20)=a(61)=a(184)=367, etc.
LINKS
EXAMPLE
n=1: 7+2 is multiple of 3, n=2: 3+2 is multiple of 5, n=5: 31+2 is multiple of 11, n=8: 83+2 is multiple of 17.
MATHEMATICA
s={}; Do[k=2; While[Mod[2+(p=Prime[k]), n]>0, k++ ]; AppendTo[s, p], {n, 3, 2001, 2}]; s
PROG
(Python)
from sympy import nextprime
def a(n):
p, m = 2, 2*n+1
while (p+2)%m: p = nextprime(p)
return p
print([a(n) for n in range(1, 61)]) # Michael S. Branicky, Jul 03 2021
(PARI) a(n) = my(p=2); while ((p+2) % (2*n+1), p = nextprime(p+1)); p; \\ Michel Marcus, Jul 03 2021
CROSSREFS
Cf. A124199.
Sequence in context: A154889 A135002 A319531 * A084714 A340820 A256779
KEYWORD
nonn
AUTHOR
Zak Seidov, May 16 2010
STATUS
approved