OFFSET
1,1
COMMENTS
Except for a(1) and a(2), all terms == 8 (mod 10).
The first three absolute differences (d) between two consecutive floor(k/5) are respectively equal to 0, 1 and 4 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*A023217(n-2) + 3. Higher terms also coincide with A265767 + 1. - Hugo Pfoertner, Mar 22 2021
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
12 is a term because 12 - 1 = 11 and 11 is prime and 12/5 = 2.4 whose floor value is 2 and 2 is also prime.
97 is not a term because 97 - 1 = 96 and 96 is not prime although floor(97/5) = 19 is prime.
Initial terms, associated primes and d:
k k - 1 floor(k/5) d
a(1) 12 11 2
a(2) 14 13 2 0
a(3) 18 17 3 1
a(4) 38 37 7 4
a(5) 68 67 13 6
a(6) 98 97 19 6
a(7) 158 157 31 12
a(8) 308 307 61 30
a(9) 338 337 67 6
a(10) 368 367 73 6
MAPLE
R:= NULL:
p:= 1: count:= 0:
while count < 100 do
p:= nextprime(p);
if isprime(floor((p+1)/5)) then
R:= R, p+1; count:= count+1
fi
od:
R; # Robert Israel, May 22 2024
MATHEMATICA
Select[Range[2, 5000, 2], And@@PrimeQ[{#-1, Floor[#/5]}]&] (* Giorgos Kalogeropoulos, Apr 01 2021 *)
PROG
(PARI) for(k = 1, 10000, if(isprime(k - 1) && isprime(k\5), print1(k", ")))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Claude H. R. Dequatre, Mar 22 2021
STATUS
approved