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%I #27 Feb 19 2024 03:42:04
%S 3,4,8,10,20,22,32,34,40,56,56,70,80,82,88,100,116,116,130,140,140,
%T 154,160,170,190,200,202,212,214,212,250,256,272,268,296,296,308,322,
%U 328,340,356,352,380,382,392,386,410,442,452,454,460,476,472,496,508,520
%N a(n) = 3p - q where p and q are consecutive primes.
%C Except for the initial term, a(n)=={2, 4} mod 6.
%C Not monotonic: a(29) = 214 > 212 = a(30), a(33) = 272 > 268 = a(34), etc. - _Charles R Greathouse IV_, Jun 03 2013
%H Paolo Xausa, <a href="/A098764/b098764.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A001043(n) - 2*A001223(n).
%F a(n) = 3*A000040(n)-A000040(n+1) = A001748(n)-A000040(n+1) = A001747(n+1)-A001223(n). - _R. J. Mathar_, Apr 22 2010
%F a(n) ~ 2n log n. - _Charles R Greathouse IV_, Jun 03 2013
%F a(n) = A100021(n) + 3. - _Hugo Pfoertner_, Nov 02 2023
%F a(n) = A062234(n) + A000040(n). - _Anthony S. Wright_, Feb 19 2024
%t ListConvolve[{-1,3},Prime[Range[100]]] (* _Paolo Xausa_, Nov 02 2023 *)
%o (PARI) a(n) = 3*prime(n) - prime(n+1) \\ _Michel Marcus_, Jun 03 2013
%Y Cf. A000040, A001043, A001223, A001748, A047235, A100021.
%K nonn,easy
%O 1,1
%A _Giovanni Teofilatto_, Sep 30 2004
%E Corrected (116 duplicated) by _R. J. Mathar_, Apr 22 2010
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