A269703 Numbers k such that prime(k) == 1 (mod 7).

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

Links

Table of n, a(n) for n=1..55.

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

Adjacent sequences: A269700 A269701 A269702 * A269704 A269705 A269706

Keyword

nonn

Author

Vincenzo Librandi, Mar 04 2016

Status

approved