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

%I A342809 #22 Apr 08 2021 11:56:51
%S A342809 8,12,14,24,54,84,114,234,264,294,354,444,504,564,654,684,744,864,954,
%T A342809 984,1164,1194,1284,1554,1584,1734,1914,2004,2154,2214,2244,2334,2394,
%U A342809 2544,2844,2964,3084,3204,3414,3594
%N A342809 Numbers k such that k-1 and round(k/5) are both prime.
%C A342809 Except for a(1) and a(2), all terms == 4 (mod 10).
%C A342809 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.
%C A342809 Subsequence of A008864, by definition. - _Michel Marcus_, Mar 22 2021
%C A342809 For n >= 3, a(n) = 5*A158318(n-2) - 1. - _Hugo Pfoertner_, Mar 22 2021
%e A342809 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.
%e A342809 235 is not a term because 235 - 1 = 234 and 234 is not a prime although 235/5 = 47 is prime.
%e A342809 Initial terms, associated primes and d:
%e A342809          k     k - 1   round(k/5)    d
%e A342809 a(1)     8       7         2
%e A342809 a(2)    12      11         2         0
%e A342809 a(3)    14      13         3         1
%e A342809 a(4)    24      23         5         2
%e A342809 a(5)    54      53        11         6
%e A342809 a(6)    84      83        17         6
%e A342809 a(7)   114     113        23         6
%e A342809 a(8)   234     233        47        24
%e A342809 a(9)   264     263        53         6
%e A342809 a(10)  294     293        59         6
%t A342809 Select[Range[2,5000,2],And@@PrimeQ[{#-1,Round[#/5]}]&] (* _Giorgos Kalogeropoulos_, Apr 01 2021 *)
%o A342809 (PARI)
%o A342809 for(k = 1,10000,if(isprime(k - 1) && isprime(k\/5),print1(k", ")))
%o A342809 (Python)
%o A342809 from sympy import isprime
%o A342809 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
%Y A342809 Cf. A000040, A007530, A007811, A014561, A259645.
%Y A342809 Cf. A008864, A158318.
%K A342809 nonn,easy
%O A342809 1,1
%A A342809 _Claude H. R. Dequatre_, Mar 22 2021