A030430 Primes of the form 10*n+1.

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

Offset: 1

Author

Warut Roonguthai

Keywords

• nonn
• easy

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. - 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

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

Primes p such that 5 divides sigma(p^4), cf. A274397. - M. F. Hasler, Jul 10 2016

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.
• Jorma K. Merikoski, Pentti Haukkanen, and Timo Tossavainen, The congruence x^n = -a^n (mod m): Solvability and related OEIS sequences, Notes. Num. Theor. Disc. Math. (2024) Vol. 30, No. 3, 516-529. See p. 519.
• N. J. A. Sloane, "A Handbook of Integer Sequences" Fifty Years Later, arXiv:2301.03149 [math.NT], 2023, p. 5.

Crossrefs

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

Cf. A001583 (subsequence).

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

Programs

Haskell

a030430 n = a030430_list !! (n-1)
a030430_list = filter ((== 1) . a010051) a017281_list
-- Reinhard Zumkeller, Apr 16 2012

Mathematica

Select[Prime@Range[210], Mod[ #, 10] == 1 &] (* Ray Chandler, Dec 06 2006 *)
Select[Range[11,1291,10],PrimeQ] (*Zak Seidov, Aug 14 2011*)

PARI

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

PARI

lista(nn) = forprime(p=11, nn, if(p%10==1, print1(p, ", "))) \\ Iain Fox, Dec 30 2017

Formula

a(n) = 10*A024912(n)+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

Intersection of A000040 and A017281. - Iain Fox, Dec 30 2017