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A030430 Primes of the form 10*n+1. 34
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, 1291 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also primes of form 5*n+1 or equivalently 5*n+6.

Primes p such that the arithmetic mean of divisors of p^4 is an integer: A000203(p^4)/A000005(p^4) = C. [From Ctibor O. Zizka, Sep 15 2008]

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

Solutions of the equation (10*n+1)'=1, where n' is the arithmetic derivative of n. [Paolo P. Lava, Nov 15 2012]

5 is quadratic residue of primes of this form. - Vincenzo Librandi, Jun 25 2014

LINKS

Michael B. Porter, Table of n, a(n) for n = 0..100000

A. Granville and G. Martin, Prime number races

FORMULA

a(n) = 10*A024912(n+1)+1 = 5*A081759(n)+6.

A104146(floor(a(n)/10)) = 1.

Union of A132230 and A132232. - Ray Chandler, Apr 07 2009

a(n) ~ 4n log n. - Charles R Greathouse IV, Sep 06 2012

MATHEMATICA

Select[Prime@Range[210], Mod[ #, 10] == 1 &] (*Chandler*)

Select[Range[11, 1291, 10], PrimeQ] (*Zak Seidov, Aug 14 2011*)

PROG

(Haskell)

a030430 n = a030430_list !! (n-1)

a030430_list = filter ((== 1) . a010051) a017281_list

-- Reinhard Zumkeller, Apr 16 2012

(PARI) is(n)==n%10==1 && isprime(n) \\ Charles R Greathouse IV, Sep 06 2012

CROSSREFS

Cf. A024912, A045453, A049511, A081759, A017281, A010051, A004615 (multiplicative closure).

Cf. A001583 (subsequence).

Sequence in context: A038351 A068871 A004615 * A059313 A040975 A188384

Adjacent sequences:  A030427 A030428 A030429 * A030431 A030432 A030433

KEYWORD

nonn,easy

AUTHOR

Warut Roonguthai

STATUS

approved

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Last modified December 17 21:30 EST 2014. Contains 252040 sequences.