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A331840
Numbers k such that 30*k-13, 30*k-11 are twin primes.
1
1, 4, 5, 7, 8, 12, 21, 28, 29, 43, 48, 50, 54, 56, 57, 60, 63, 67, 68, 70, 75, 76, 89, 90, 106, 109, 116, 118, 119, 126, 131, 138, 139, 141, 145, 151, 152, 155, 160, 166, 181, 183, 189, 196, 207, 228, 232, 238, 244, 249, 250, 252, 259, 263, 270, 280, 285, 287
OFFSET
1,2
COMMENTS
All twin primes > 7 have the form 30*k-{13,11}, or 30*k +-1 (A176114), or 30*k+{11,13} (A089160).
All twin primes > 7 with least significant decimal digit 7 have the form 30*k-13.
All twin primes > 7 with least significant decimal digit 3 have the form 30*k+13.
FORMULA
a(n) = A089161(n)+1.
EXAMPLE
1 is a term because 1*30 - 13 = 17 = prime(6) and 1*30 - 11 = 19 = prime(7).
4 is a term because 4*30 - 13 = 107 = prime(28) and 4*30 - 11 = 109 = prime(29).
5 is a term because 5*30 - 13 = 137 = prime(33) and 5*30 - 11 = 139 = prime(34).
MATHEMATICA
Select[Range[300], And @@ PrimeQ[30*# - {11, 13}] &] (* Amiram Eldar, Feb 29 2020 *)
PROG
(Rexx)
S = 1
do N = 2 while length( S ) < 255
if NOPRIME( N*30 -13 ) then iterate N
if NOPRIME( N*30 -11 ) then iterate N
S = S || ', ' N
end N
say S
(PARI) isok(k) = isprime(30*k-13) && isprime(30*k-11); \\ Michel Marcus, Feb 29 2020
KEYWORD
nonn,easy
AUTHOR
Frank Ellermann, Feb 26 2020
STATUS
approved