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Complement of the pentagonal numbers.
3

%I #22 Oct 05 2024 10:26:09

%S 2,3,4,6,7,8,9,10,11,13,14,15,16,17,18,19,20,21,23,24,25,26,27,28,29,

%T 30,31,32,33,34,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,52,53,54,

%U 55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,93

%N Complement of the pentagonal numbers.

%H Kevin Ryde, <a href="/A183217/b183217.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = n + floor(1/2+(2n/3)^(1/2)).

%F a(n) = n + A111651(n). - _Kevin Ryde_, Aug 31 2024

%e The pentagonal numbers A000326 = (1,5,12,22,35,...), so that this sequence = (2,3,4,6,7,8,9,10,11,13,14,...).

%t Table[n+Floor[1/2+(2n/3)^(1/2)], {n,100}]

%o (PARI) a(n) = n + sqrtint(24*n)\/6; \\ _Kevin Ryde_, Aug 31 2024

%o (Python)

%o from math import isqrt

%o def A183217(n): return n+(isqrt((n<<3)//3)+1>>1) # _Chai Wah Wu_, Oct 05 2024

%Y Cf. A000326, A111651.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jan 01 2011