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%I #44 Feb 19 2024 03:05:25
%S 1,1,3,3,9,9,15,15,17,27,25,33,39,39,41,47,57,55,63,69,67,75,77,81,93,
%T 99,99,105,105,99,123,125,135,129,147,145,151,159,161,167,177,171,189,
%U 189,195,187,199,219,225,225,227,237,231,245,251,257,267,265,273,279
%N From Bertrand's postulate: a(n) = 2*prime(n) - prime(n+1).
%C The theorem that a(n) > 0 for all n is known as "Bertrand's Postulate", and was proved by Tchebycheff in 1852.
%C The analog for Ramanujan primes is Paksoy's theorem that 2*R(n) - R(n+1) > 0 for n > 1. See A233822. - _Jonathan Sondow_, Dec 16 2013
%D J. V. Uspensky and M. A. Heaslet, Elementary Number Theory, McGraw-Hill, NY, 1939.
%H Harry J. Smith, <a href="/A062234/b062234.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A000040(n) - A001223(n). - _Zak Seidov_, Sep 07 2012
%F a(n) = 2*A000040(n) - A000040(n+1). - _Zak Seidov_, May 12 2020
%F a(n) = A098764(n) - A000040(n). - _Anthony S. Wright_, Feb 19 2024
%p a:= n-> (p-> 2*p(n)-p(n+1))(ithprime):
%p seq(a(n), n=1..60); # _Alois P. Heinz_, Feb 09 2022
%o (PARI) a(n) = 2*prime(n) - prime(n + 1); \\ _Harry J. Smith_, Aug 03 2009
%o (Haskell)
%o a062234 n = a062234_list !! (n-1)
%o a062234_list = zipWith (-) (map (* 2) a000040_list) (tail a000040_list)
%o -- _Reinhard Zumkeller_, May 31 2015
%Y Cf. A000040, A001223, A215808 (prime terms), A233822.
%Y Cf. A098764, A100484, A258383 (run lengths), A258432, A258469, A257762, A258449, A257892, A257951.
%K easy,nonn
%O 1,3
%A _Reinhard Zumkeller_, Jun 29 2001
%E Edited by _N. J. A. Sloane_, Feb 24 2023
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