A342809 Numbers k such that k-1 and round(k/5) are both prime.

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

Links

Table of n, a(n) for n=1..40.

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

Cf. A000040, A007530, A007811, A014561, A259645.

Cf. A008864, A158318.

Sequence in context: A107071 A114414 A032455 * A279963 A050275 A363863

Adjacent sequences: A342806 A342807 A342808 * A342810 A342811 A342812

Keyword

nonn,easy

Author

Claude H. R. Dequatre, Mar 22 2021

Status

approved