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A243111 Difference between the smallest triangular number >= n-th prime and the n-th prime. 1

%I

%S 1,0,1,3,4,2,4,2,5,7,5,8,4,2,8,2,7,5,11,7,5,12,8,2,8,4,2,13,11,7,9,5,

%T 16,14,4,2,14,8,4,17,11,9,19,17,13,11,20,8,4,2,20,14,12,2,19,13,7,5,

%U 23,19,17,7,18,14,12,8,20,14,4,2,25,19,11,5,27,23,17,9,5,26,16,14,4,2,26

%N Difference between the smallest triangular number >= n-th prime and the n-th prime.

%H Jens Kruse Andersen, <a href="/A243111/b243111.txt">Table of n, a(n) for n = 1..10000</a>

%e x, 0 , x , x , x

%e 0 0 0 0 0 0 x x x x

%e 0 0 0 0 0 0 0 0 x

%e 0 0 0 0 0 0 0 0

%e 0 0 0 0 0

%e P(n) = 2,3,5,7,11,...

%e x -> we need respectively 1, 0, 1, 3 and 4 numbers to complete the whole triangle.

%t Module[{upto=100,tnos},tnos=Accumulate[Range[Ceiling[(Sqrt[8*Prime[upto]+ 1]- 1)/2]]];Table[SelectFirst[tnos,#>=Prime[n]&]-Prime[n],{n,upto}]] (* _Harvey P. Dale_, Jan 15 2015 *)

%o (PARI)

%o a(n)=k=1;while(k*(k+1)/2<prime(n),k++);return(k*(k+1)/2-prime(n))

%o vector(100,n,a(n)) \\ _Derek Orr_, Aug 21 2014

%Y Cf. A000040, A002262, A000217.

%K nonn,easy

%O 1,4

%A _Odimar Fabeny_, Aug 20 2014

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Last modified August 15 12:33 EDT 2020. Contains 336499 sequences. (Running on oeis4.)