A076274 - OEIS

%I #42 Nov 28 2023 14:45:33

%S 1,3,5,9,13,21,25,33,37,45,57,61,73,81,85,93,105,117,121,133,141,145,

%T 157,165,177,193,201,205,213,217,225,253,261,273,277,297,301,313,325,

%U 333,345,357,361,381,385,393,397,421,445,453,457,465,477,481,501,513,525,537,541

%N 2p-1 where p is 1 or a prime.

%H Vincenzo Librandi, <a href="/A076274/b076274.txt">Table of n, a(n) for n = 1..1000</a>

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

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

%F 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

%F a(n) = 2*A008578(n) - 1. - _Alois P. Heinz_, Nov 28 2023

%t Join[{1},2*Prime[Range[100]]-1] (* _Harvey P. Dale_, Nov 29 2015 *)

%o (PARI) a(n)=if(n>1,2*prime(n-1)-1,1) \\ _Charles R Greathouse IV_, Apr 29 2015

%o (Magma) [2*NthPrime(n-1)-1: n in [1..60]]; // _Vincenzo Librandi_, Jul 31 2017

%Y Positions of squares in A076271.

%Y Subsequence of A186621 and of A005408.

%Y Cf. A000010, A000720, A002033, A008578.

%K nonn,easy

%O 1,2

%A _Reinhard Zumkeller_, Oct 04 2002

%E New definition from _Thomas Baruchel_, Oct 21 2003

%E Offset changed from _Vincenzo Librandi_, Jul 31 2017