A379207 a(n) = 2*prime(n+1) - (prime(n+1) - prime(n))^2.

5, 6, 10, 6, 22, 18, 34, 30, 22, 58, 38, 66, 82, 78, 70, 82, 118, 98, 126, 142, 122, 150, 142, 130, 186, 202, 198, 214, 210, 58, 246, 238, 274, 198, 298, 278, 290, 318, 310, 322, 358, 282, 382, 378, 394, 278, 302, 438, 454, 450, 442, 478, 402, 478, 490, 502, 538, 518, 546, 562

Offset

1,1

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Jacques Grah, Conditional Bounds for Prime Gaps with Applications, arXiv:2412.12311 [math.NT], 2024.

Formula

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

Mathematica

Array[2*Prime[# + 1] - (Prime[# + 1] - Prime[#])^2 &, 120] (* Michael De Vlieger, Dec 18 2024 *)

Prog

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

Crossrefs

Cf. A000040, A001223.

Sequence in context: A273039 A019125 A019205 * A191472 A189056 A340325

Adjacent sequences: A379192 A379193 A379194 * A379209 A379215 A379218

Keyword

nonn,new

Author

Michel Marcus, Dec 18 2024

Status

approved