login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

a(n) = 2*prime(n+1) - (prime(n+1) - prime(n))^2.
1

%I #8 Dec 18 2024 09:41:27

%S 5,6,10,6,22,18,34,30,22,58,38,66,82,78,70,82,118,98,126,142,122,150,

%T 142,130,186,202,198,214,210,58,246,238,274,198,298,278,290,318,310,

%U 322,358,282,382,378,394,278,302,438,454,450,442,478,402,478,490,502,538,518,546,562

%N a(n) = 2*prime(n+1) - (prime(n+1) - prime(n))^2.

%H Michael De Vlieger, <a href="/A379207/b379207.txt">Table of n, a(n) for n = 1..10000</a>

%H Jacques Grah, <a href="https://arxiv.org/abs/2412.12311">Conditional Bounds for Prime Gaps with Applications</a>, arXiv:2412.12311 [math.NT], 2024.

%F a(n) = 2*A000040(n+1) - A001223(n)^2.

%t Array[2*Prime[# + 1] - (Prime[# + 1] - Prime[#])^2 &, 120] (* _Michael De Vlieger_, Dec 18 2024 *)

%o (PARI) a(n) = 2*prime(n+1) - (prime(n+1) - prime(n))^2;

%Y Cf. A000040, A001223.

%K nonn,new

%O 1,1

%A _Michel Marcus_, Dec 18 2024