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

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%I A045453 #25 Sep 08 2022 08:44:56
%S A045453 5,11,31,41,61,71,101,131,151,181,191,211,241,251,271,281,311,331,401,
%T A045453 421,431,461,491,521,541,571,601,631,641,661,691,701,751,761,811,821,
%U A045453 881,911,941,971,991,1021,1031,1051,1061,1091,1151,1171,1181,1201,1231
%N A045453 Primes congruent to {0, 1} mod 5.
%C A045453 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
%H A045453 Vincenzo Librandi, <a href="/A045453/b045453.txt">Table of n, a(n) for n = 1..1000</a>
%F A045453 a(n) = A030430(n-1) for all n >= 2. - _M. F. Hasler_, Jan 15 2018
%e A045453 a(1) = 5 is the first primes that is congruent to 0 or 1, modulo 5.
%e A045453 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.
%e A045453 a(10^k) = (181, 2791, 38201, 479771, 5803381, 67881871, 776580131, ...) for k = 1, 2, 3, ...
%t A045453 Select[Prime@Range[210], MemberQ[{0, 1}, Mod[ #, 5]] &] (* _Ray Chandler_, Dec 06 2006 *)
%o A045453 (Magma) [ p: p in PrimesUpTo(1300) | p mod 5 in {0, 1} ]; // _Vincenzo Librandi_, Aug 13 2012
%o A045453 (PARI) A045453_vec(Nmax)=select( p->p%5<2, primes([1,Nmax])) \\ or:
%o A045453 A045453(n)=forprime(p=1,,p%5>1||n--||return(p)) \\ _M. F. Hasler_, Jan 15 2018
%Y A045453 Same as A030430 with addition of the only prime congruent to 0 (mod 5), a(1) = 5.
%Y A045453 Cf. A000040.
%K A045453 nonn,easy
%O A045453 1,1
%A A045453 _N. J. A. Sloane_
%E A045453 Extended by _Ray Chandler_, Nov 28 2003
%E A045453 Checked by Neven Juric (neven.juric(AT)apis-it.hr), Feb 04 2008
%E A045453 Edited and a(1000) double checked by _M. F. Hasler_, Jan 15 2018