login
A342809
Numbers k such that k-1 and round(k/5) are both prime.
0
8, 12, 14, 24, 54, 84, 114, 234, 264, 294, 354, 444, 504, 564, 654, 684, 744, 864, 954, 984, 1164, 1194, 1284, 1554, 1584, 1734, 1914, 2004, 2154, 2214, 2244, 2334, 2394, 2544, 2844, 2964, 3084, 3204, 3414, 3594
OFFSET
1,1
COMMENTS
Except for a(1) and a(2), all terms == 4 (mod 10).
The first three absolute differences (d) between two consecutive rounded (k/5) are respectively equal to 0, 1 and 2 and all the others to 6 or a multiple of 6.
Subsequence of A008864, by definition. - Michel Marcus, Mar 22 2021
For n >= 3, a(n) = 5*A158318(n-2) - 1. - Hugo Pfoertner, Mar 22 2021
EXAMPLE
8 is a term because 8 - 1 = 7 and 7 is prime and 8/5 = 1.6 which when rounded gives 2 and 2 is also prime.
235 is not a term because 235 - 1 = 234 and 234 is not a prime although 235/5 = 47 is prime.
Initial terms, associated primes and d:
k k - 1 round(k/5) d
a(1) 8 7 2
a(2) 12 11 2 0
a(3) 14 13 3 1
a(4) 24 23 5 2
a(5) 54 53 11 6
a(6) 84 83 17 6
a(7) 114 113 23 6
a(8) 234 233 47 24
a(9) 264 263 53 6
a(10) 294 293 59 6
MATHEMATICA
Select[Range[2, 5000, 2], And@@PrimeQ[{#-1, Round[#/5]}]&] (* Giorgos Kalogeropoulos, Apr 01 2021 *)
PROG
(PARI)
for(k = 1, 10000, if(isprime(k - 1) && isprime(k\/5), print1(k", ")))
(Python)
from sympy import isprime
A342809_list = [k for k in range(1, 10**5) if isprime(k-1) and isprime(k//5+int(k % 5 > 2))] # Chai Wah Wu, Apr 08 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved