A045453 Primes congruent to {0, 1} mod 5.

5, 11, 31, 41, 61, 71, 101, 131, 151, 181, 191, 211, 241, 251, 271, 281, 311, 331, 401, 421, 431, 461, 491, 521, 541, 571, 601, 631, 641, 661, 691, 701, 751, 761, 811, 821, 881, 911, 941, 971, 991, 1021, 1031, 1051, 1061, 1091, 1151, 1171, 1181, 1201, 1231

Offset

1,1

Comments

Being a subset of A141158, this is also a subset of the primes of form x^2 - 5y^2. - Tito Piezas III, Dec 28 2008

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Formula

a(n) = A030430(n-1) for all n >= 2. - M. F. Hasler, Jan 15 2018

Example

a(1) = 5 is the first primes that is congruent to 0 or 1, modulo 5.
a(2) = 11 is the first prime congruent to 1 modulo 5, and therefore (since there is no other prime congruent to 0 mod 5) the second term of this sequence.
a(10^k) = (181, 2791, 38201, 479771, 5803381, 67881871, 776580131, ...) for k = 1, 2, 3, ...

Mathematica

Select[Prime@Range[210], MemberQ[{0, 1}, Mod[ #, 5]] &] (* Ray Chandler, Dec 06 2006 *)

Prog

(Magma) [ p: p in PrimesUpTo(1300) | p mod 5 in {0, 1} ]; // Vincenzo Librandi, Aug 13 2012
(PARI) A045453_vec(Nmax)=select( p->p%5<2, primes([1, Nmax])) \\ or:
A045453(n)=forprime(p=1, , p%5>1||n--||return(p)) \\ M. F. Hasler, Jan 15 2018

Crossrefs

Same as A030430 with addition of the only prime congruent to 0 (mod 5), a(1) = 5.

Cf. A000040.

Sequence in context: A239842 A092963 A191069 * A052228 A371670 A105910

Adjacent sequences: A045450 A045451 A045452 * A045454 A045455 A045456

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Extended by Ray Chandler, Nov 28 2003

Checked by Neven Juric (neven.juric(AT)apis-it.hr), Feb 04 2008

Edited and a(1000) double checked by M. F. Hasler, Jan 15 2018

Status

approved