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A269703
Numbers k such that prime(k) == 1 (mod 7).
2
10, 14, 20, 30, 31, 45, 47, 52, 60, 68, 75, 82, 87, 90, 94, 101, 113, 115, 120, 122, 126, 132, 134, 144, 153, 156, 162, 163, 169, 177, 183, 192, 209, 213, 220, 226, 233, 239, 250, 251, 262, 267, 269, 288, 295, 304, 306, 315, 320, 324, 330, 337, 342, 344, 346
OFFSET
1,1
COMMENTS
The asymptotic density of this sequence is 1/6 (by Dirichlet's theorem). - Amiram Eldar, Mar 01 2021
FORMULA
a(n) ~ 6*n. - Charles R Greathouse IV, Sep 20 2016 [Corrected by Amiram Eldar, Mar 01 2021]
EXAMPLE
a(1) = 10 because prime(10) = 29 and 29 == 1 (mod 7).
MATHEMATICA
Select[Range[500], Mod[Prime[#], 7] == 1 &]
PROG
(Magma) [n: n in [1..500] | NthPrime(n) mod 7 eq 1];
(PARI) lista(nn) = for(n=1, nn, if(Mod(prime(n), 7)==1, print1(n, ", "))); \\ Altug Alkan, Mar 04 2016
CROSSREFS
The associated primes are in A004619.
Sequences of numbers n such that prime(n) == 1 (mod k): A091178 (k=3,6), A080147 (k=4), A049511 (k=5,10), this sequence (k=7), A269704 (k=8), A269705 (k=9).
Sequence in context: A272375 A246473 A063920 * A057487 A073486 A073487
KEYWORD
nonn
AUTHOR
Vincenzo Librandi, Mar 04 2016
STATUS
approved