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A030433 Primes of form 10*k + 9. 31
19, 29, 59, 79, 89, 109, 139, 149, 179, 199, 229, 239, 269, 349, 359, 379, 389, 409, 419, 439, 449, 479, 499, 509, 569, 599, 619, 659, 709, 719, 739, 769, 809, 829, 839, 859, 919, 929, 1009, 1019, 1039, 1049, 1069, 1109, 1129, 1229, 1249, 1259, 1279, 1289 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also primes of form 5*k + 4.

5 is quadratic residue of primes of form 10*k-1. - Vincenzo Librandi, Jun 25 2014

Also, primes p such that 5 divides sigma(p), cf. A274397. - M. F. Hasler, Jul 10 2016

Conjecture: Primes p such that ((x+1)^5-1)/x has 2 distinct irreducible factors of degree 2 over GF(p). - Federico Provvedi, Apr 01 2018

The digital root of a(n) is 1, 2, 4, 5, 7 or 8. - Muniru A Asiru, Apr 28 2018

LINKS

Michael B. Porter, Table of n, a(n) for n = 1..100000

A. Granville and G. Martin, Prime number races, arXiv:math/0408319 [math.NT], 2004.

Erika Klarreich, Mathematicians Discover Prime Conspiracy, Quanta Magazine, 2016.

R. J. Lemke Oliver and K. Soundararajan, Unexpected biases in the distribution of consecutive primes, arXiv:1603.03720 [math.NT], 2016.

FORMULA

a(n) = 10*A102700(n) + 9.

Union of A132234 and A132236. - Ray Chandler, Apr 07 2009

Intersection of A000040 and A017377. - Iain Fox, Dec 30 2017

MAPLE

select(isprime, [seq(10*n+9, n=1..500)]); # Muniru A Asiru, Apr 27 2018

MATHEMATICA

Select[Prime@Range[210], Mod[ #, 10] == 9 &] (* Ray Chandler, Nov 07 2006 *)

Select[Range[9, 1300, 10], PrimeQ] (* Harvey P. Dale, Jun 01 2012 *)

Prime@Flatten@Position[Length@FactorList[((1+d)^5-1)/d, Modulus->#]&/@Prime@Range@200, 3] (* Federico Provvedi, Apr 04 2018 *)

PROG

(PARI) select(n->n%10==9, primes(100)) \\ Charles R Greathouse IV, Apr 29 2015

(PARI) for(n=1, 1e3, if(isprime(p=10*n+9), print1(p, ", "))); \\ Altug Alkan, Apr 19 2018

(GAP) Filtered(List([1..500], n->10*n+9), IsPrime); # Muniru A Asiru, Apr 27 2018

CROSSREFS

Cf. A045457, A049510, A102700.

Sequence in context: A084666 A242265 A004618 * A242550 A141311 A090148

Adjacent sequences:  A030430 A030431 A030432 * A030434 A030435 A030436

KEYWORD

nonn

AUTHOR

Warut Roonguthai

EXTENSIONS

Extended by Ray Chandler, Nov 07 2006

STATUS

approved

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Last modified May 24 03:44 EDT 2018. Contains 304500 sequences. (Running on oeis4.)