Search: id:A005382
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%I A005382 M0849
%S A005382 2,3,7,19,31,37,79,97,139,157,199,211,229,271,307,331,337,367,379,
%T A005382 439,499,547,577,601,607,619,661,691,727,811,829,877,937,967,997,
%U A005382 1009,1069,1171,1237,1279,1297,1399,1429,1459,1531,1609,1627,1657
%N A005382 Numbers n such that n and 2n-1 are primes.
%C A005382 Sequence gives values of n such sum(i=1,n,GCD(n,i))=A018804(n) is prime. 
               - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 25 2002
%C A005382 Let q = 2n-1. For these n (and q), the sum of two cyclotomic polynomials 
               can be written as a product of cyclotomic polynomials and as a cyclotomic 
               polynomial in x^2: Phi(q,x) + Phi(2q,x) = 2 Phi(n,x) Phi(2n,x) = 
               2 Phi(n,x^2). - T. D. Noe (noe(AT)sspectra.com), Nov 04 2003
%C A005382 Numbers n such that the n-th Hexagonal number A000384(n) = n*(2*n-1) 
               is semiprime. {A005382} = {n such that A000384(n) is an element of 
               A001358}. - Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 14 2006
%D A005382 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards Applied Math. Series 55, 1964 (and various 
               reprintings), p. 870.
%D A005382 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005382 T. D. Noe, <a href="b005382.txt">Table of n, a(n) for n=1..10000</a>
%H A005382 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A005382 J. Perry, <a href="http://www.users.globalnet.co.uk/~perry/maths/germainprimes/
               germainprimes.htm">Germain Primes</a>
%F A005382 a(n) = A129521(n)/A005383(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Apr 19 2007
%p A005382 f := proc(Q) local t1,i,j; t1 := []; for i from 1 to 500 do j := ithprime(i); 
               if isprime(2*j-Q) then t1 := [op(t1),j]; fi; od: t1; end; f(1);
%t A005382 Select[Prime[Range[300]], PrimeQ[2#-1]&]
%Y A005382 Cf. A005383, A057326, A057327, A057328, A057329, A057330, A005603, A063908, 
               A023204.
%Y A005382 Cf. A000384, A001358.
%Y A005382 Sequence in context: A074855 A038935 A073640 this_sequence A113165 A128025 
               A092064
%Y A005382 Adjacent sequences: A005379 A005380 A005381 this_sequence A005383 A005384 
               A005385
%K A005382 nonn,easy
%O A005382 1,1
%A A005382 N. J. A. Sloane (njas(AT)research.att.com).

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