cp's OEIS Frontend

A030430 Primes of the form 10*n+1.

%I A030430 #75 Oct 08 2024 16:19:13
%S A030430 11,31,41,61,71,101,131,151,181,191,211,241,251,271,281,311,331,401,
%T A030430 421,431,461,491,521,541,571,601,631,641,661,691,701,751,761,811,821,
%U A030430 881,911,941,971,991,1021,1031,1051,1061,1091,1151,1171,1181,1201,1231,1291
%N A030430 Primes of the form 10*n+1.
%C A030430 Also primes of form 5*n+1 or equivalently 5*n+6.
%C A030430 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
%C A030430 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
%C A030430 5 is quadratic residue of primes of this form. - _Vincenzo Librandi_, Jun 25 2014
%C A030430 Primes p such that 5 divides sigma(p^4), cf. A274397. - _M. F. Hasler_, Jul 10 2016
%H A030430 Michael B. Porter, <a href="/A030430/b030430.txt">Table of n, a(n) for n = 1..100000</a>
%H A030430 A. Granville and G. Martin, <a href="https://arxiv.org/abs/math/0408319">Prime number races</a>, arXiv:math/0408319 [math.NT], 2004.
%H A030430 Jorma K. Merikoski, Pentti Haukkanen, and Timo Tossavainen, <a href="https://doi.org/10.7546/nntdm.2024.30.3.516-529">The congruence x^n = -a^n (mod m): Solvability and related OEIS sequences</a>, Notes. Num. Theor. Disc. Math. (2024) Vol. 30, No. 3, 516-529. See p. 519.
%H A030430 N. J. A. Sloane, <a href="https://arxiv.org/abs/2301.03149">"A Handbook of Integer Sequences" Fifty Years Later</a>, arXiv:2301.03149 [math.NT], 2023, p. 5.
%F A030430 a(n) = 10*A024912(n)+1 = 5*A081759(n)+6.
%F A030430 A104146(floor(a(n)/10)) = 1.
%F A030430 Union of A132230 and A132232. - _Ray Chandler_, Apr 07 2009
%F A030430 a(n) ~ 4n log n. - _Charles R Greathouse IV_, Sep 06 2012
%F A030430 Intersection of A000040 and A017281. - _Iain Fox_, Dec 30 2017
%t A030430 Select[Prime@Range[210], Mod[ #, 10] == 1 &] (* _Ray Chandler_, Dec 06 2006 *)
%t A030430 Select[Range[11,1291,10],PrimeQ] (*_Zak Seidov_, Aug 14 2011*)
%o A030430 (Haskell)
%o A030430 a030430 n = a030430_list !! (n-1)
%o A030430 a030430_list = filter ((== 1) . a010051) a017281_list
%o A030430 -- _Reinhard Zumkeller_, Apr 16 2012
%o A030430 (PARI) is(n)=n%10==1 && isprime(n) \\ _Charles R Greathouse IV_, Sep 06 2012
%o A030430 (PARI) lista(nn) = forprime(p=11, nn, if(p%10==1, print1(p, ", "))) \\ _Iain Fox_, Dec 30 2017
%Y A030430 Cf. A024912, A045453, A049511, A081759, A017281, A010051, A004615 (multiplicative closure).
%Y A030430 Cf. A001583 (subsequence).
%Y A030430 Union of A132230 and A132232. - _Ray Chandler_, Apr 07 2009
%K A030430 nonn,easy
%O A030430 1,1
%A A030430 _Warut Roonguthai_