A145826 Arises from critical number of finite Abelian groups.

7, 8, 11, 14, 19, 21, 26, 29, 34, 41, 43, 50, 55, 57, 62, 68, 75, 77, 84, 89, 91, 98, 102, 109, 117, 122, 124, 128, 131, 135, 150, 155, 161, 163, 174, 176, 183, 189, 194, 200, 206, 209, 219, 221, 226, 228, 241, 254, 258, 260, 264, 271, 273, 283, 290, 296, 302

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

P. Erdős and H. Heilbronn, On the addition of residue classes modulo p, Acta Arith. 9 (1964), 149 - 159.

Michael Freeze, Weidong Gao and Alfred Geroldinger, The critical number of finite Abelian groups, arXiv:0810.3223 [math.NT], Oct 17, 2008.

Formula

a(n) = prime(n) + floor(2*(sqrt(prime(n)+2))) + 1, where prime(n) = n-th prime = A000040(n).

a(n) >= A000006(n) + A008864(n). - R. J. Mathar, Jan 05 2009

Example

a(10) = prime(10) + floor(2*sqrt(prime(10)+2)) + 1 = 29 + floor(2*sqrt(29+2)) + 1 = 29 + floor(2*5.56776436) + 1 = 29 + floor(11.1355287) + 1 = 29 + 11 + 1 = 41.

Maple

map(t -> t + floor(2*sqrt(t+2))+1, [seq(ithprime(i), i=1..100)]); # Robert Israel, Feb 02 2016

Mathematica

Table[Prime[n] + Floor[2 (Sqrt[Prime[n] + 2])] + 1, {n, 60}] (* Vincenzo Librandi, Feb 02 2016 *)

Prog

(PARI) a(n) = prime(n) + floor(2*(sqrt(prime(n)+2))) + 1; \\ Michel Marcus, Feb 01 2016
(Magma) [NthPrime(n)+Floor(2*(Sqrt(NthPrime(n)+2)))+1: n in [1..80]]; // Vincenzo Librandi, Feb 02 2016

Crossrefs

Cf. A000040.

Sequence in context: A309592 A090385 A350694 * A102963 A117619 A226977

Adjacent sequences: A145823 A145824 A145825 * A145827 A145828 A145829

Keyword

easy,nonn,changed

Author

Jonathan Vos Post, Oct 20 2008

Extensions

More terms from R. J. Mathar, Jan 05 2009

Status

approved