A076274 2p-1 where p is 1 or a prime.

1, 3, 5, 9, 13, 21, 25, 33, 37, 45, 57, 61, 73, 81, 85, 93, 105, 117, 121, 133, 141, 145, 157, 165, 177, 193, 201, 205, 213, 217, 225, 253, 261, 273, 277, 297, 301, 313, 325, 333, 345, 357, 361, 381, 385, 393, 397, 421, 445, 453, 457, 465, 477, 481, 501, 513, 525, 537, 541

Offset: 1

Author

Reinhard Zumkeller, Oct 04 2002

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Positions of squares in A076271.

Subsequence of A186621 and of A005408.

Cf. A000010, A000720, A002033, A008578.

Programs

Magma

[2*NthPrime(n-1)-1: n in [1..60]]; // Vincenzo Librandi, Jul 31 2017

Mathematica

Join[{1},2*Prime[Range[100]]-1] (* Harvey P. Dale, Nov 29 2015 *)

PARI

a(n)=if(n>1,2*prime(n-1)-1,1) \\ Charles R Greathouse IV, Apr 29 2015

Formula

A076271(a(n)) = A008578(n)^2 for all n.

a(n+1) - a(n) = 2*A075526(n) for all n.

G.f.: 1 + Sum_{ j>=1 } Sum_{ k>=1 } x^(pi(k/2)+j), where pi(k) is the prime counting function. - Benedict W. J. Irwin, Jun 13 2016

a(n) = 2*A008578(n) - 1. - Alois P. Heinz, Nov 28 2023

Extensions

New definition from Thomas Baruchel, Oct 21 2003

Offset changed from Vincenzo Librandi, Jul 31 2017