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3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Rayes et al. prove that the a(n)-th Chebyshev-T polynomial, divided by x, is irreducible over the integers.
Intersection of A005408 and A000040. [From Reinhard Zumkeller, Oct 14 2008]
Smallest prime>n-th prime. [From Juri-Stepan Gerasimov, Oct 29 2009]
Primes which are the sum of two consecutive numbers. [From Juri-Stepan Gerasimov, Nov 07 2009]
Primes==-+1 mod 4. [From Juri-Stepan Gerasimov, Apr 27 2010]
a(n) = A053670(A179675(n)) and a(n) <> A053670(m) for m < A179675(n). [From Reinhard Zumkeller, Jul 23 2010]
Triads of the form <2*a(n+1), a(n+1), 3*a(n+1)> like <6,3,9>, <10,5,15>, <14,7,21> appear in the EKG sequence A064413, see Theorem (3) there. - Paul Curtz, Feb 13 2011.
Complement of A065090; abs(A151763(a(n))) = 1. [Reinhard Zumkeller, Oct 06 2011]
Right edge of the triangle in A065305. [Reinhard Zumkeller, Jan 30 2012]
Numbers with two odd divisors. - Omar E. Pol, Mar 24 2012
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LINKS
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Harry J. Smith, Table of n, a(n) for n = 1..1000
M. O. Rayes, V. Trevisan and P. S. Wang, Factorization of Chebyshev Polynomials
Eric Weisstein's World of Mathematics, Prime Number.
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MAPLE
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A065091 := proc(n) RETURN(ithprime(n+1)) end:
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MATHEMATICA
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Prime[Range[2, 33]] [From Vladimir Joseph Stephan Orlovsky, Aug 22 2008]
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PROG
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(PARI) { for (n=1, 1000, write("b065091.txt", n, " ", prime(n + 1)) ) } [From Harry J. Smith, Oct 06 2009]
(PARI) The program below is supposedly valid for generating primes for n>=3; it is based on the comment in A075888: "For n>=3, prime(n+1)^2-prime(n)^2 is always divisible by 24" j=[]; for(n=0, 500, if((floor(sqrt(4!*(n+1) + 1))) == ceil(sqrt(4!*(n+1) + 1)), if(isprime(floor(sqrt(4!*(n+1) + 1))), j=concat(j, floor(sqrt(4!*(n+1) + 1)))))); j [From Alexander R. Povolotsky, Sep 16 2008]
(Haskell)
a065091 n = a065091_list !! (n-1)
a065091_list = tail a000040_list -- Reinhard Zumkeller, Jan 30 2012
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CROSSREFS
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Cf. A000040, A033270.
Sequence in context: A176997 A006005 * A160656 A065380 A211075 A038134
Adjacent sequences: A065088 A065089 A065090 * A065092 A065093 A065094
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KEYWORD
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nonn,easy
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Nov 12 2001
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EXTENSIONS
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More terms from Francisco Salinas (franciscodesalinas(AT)hotmail.com), Jan 05 2002
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STATUS
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approved
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