A331840 - OEIS

%I #36 Sep 06 2023 13:41:30

%S 1,4,5,7,8,12,21,28,29,43,48,50,54,56,57,60,63,67,68,70,75,76,89,90,

%T 106,109,116,118,119,126,131,138,139,141,145,151,152,155,160,166,181,

%U 183,189,196,207,228,232,238,244,249,250,252,259,263,270,280,285,287

%N Numbers k such that 30*k-13, 30*k-11 are twin primes.

%C All twin primes > 7 have the form 30*k-{13,11}, or 30*k +-1 (A176114), or 30*k+{11,13} (A089160).

%C All twin primes > 7 with least significant decimal digit 7 have the form 30*k-13.

%C All twin primes > 7 with least significant decimal digit 3 have the form 30*k+13.

%F a(n) = A089161(n)+1.

%e 1 is a term because 1*30 - 13 =  17 = prime(6)  and 1*30 - 11 =  19 = prime(7).

%e 4 is a term because 4*30 - 13 = 107 = prime(28) and 4*30 - 11 = 109 = prime(29).

%e 5 is a term because 5*30 - 13 = 137 = prime(33) and 5*30 - 11 = 139 = prime(34).

%t Select[Range[300], And @@ PrimeQ[30*# - {11, 13}] &] (* _Amiram Eldar_, Feb 29 2020 *)

%o (Rexx)

%o S = 1

%o do N = 2 while length( S ) < 255

%o    if NOPRIME( N*30 -13 )  then  iterate N

%o    if NOPRIME( N*30 -11 )  then  iterate N

%o    S = S || ',' N

%o end N

%o say S

%o (PARI) isok(k) = isprime(30*k-13) && isprime(30*k-11); \\ _Michel Marcus_, Feb 29 2020

%Y Cf. A089160, A089161, A176114, A332772.

%Y Cf. A000040, A001097, A002822, A132242, A282323, A282324.

%K nonn,easy

%O 1,2

%A _Frank Ellermann_, Feb 26 2020